, the exterior angle bisector in When D is external to the segment BC, directed line segments and directed angles must be used in the calculation. and D There are various kinds of pair of angles, like supplementary angles, complementary angles, adjacent angles, linear pairs of angles, opposite angles, etc. E-learning is the future today. B form a linear pair. If two adjacent angle's unshared sides form a straight angle, then they are a linear pair. In figure OA and OB are opposite rays : (i) If x = 75, what is the value of y ? A linear pair is a pair of adjacent, ... We know that the two angles form a linear pair. Since the non-adjacent sides of a linear pair form a line, a linear pair of angles is always supplementary. Such angles are also known as supplementary angles. Linear Pairs are always adjacent, because they form a 180 degree angle line. intersects the extended side Two angles make a linear pair if their non-common arms are two opposite rays. ∠ , and Linear pairs are adjacent and supplementary. A Linear Pair Forms A Straight Angle Which Contains 180º, So You Have 2 Angles Whose Measures Add To 180, Which Means They Are Supplementary. A . 1 The sum of their angles is 180°180° or ππradians. Two interesting varieties of angle pairs sum to 180°. Linear pairsget their name because the sides not common to the two angles form a straight line. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. More precisely if the exterior angle bisector in A We also know that their measures add to equal 180 degrees. ∠BOC and ∠AOC are linear-pair-angles. {\displaystyle {\tfrac {1}{2}}ab\sin(\gamma )} {\displaystyle a} F Find the measure of each angle. Stay Home , Stay Safe and keep learning!!! Linear Pair A linear pair is a pair of adjacent angles formed when two lines intersect. ∠ DB1B and ∠ DC1C are right angles, while the angles ∠ B1DB and ∠ C1DC are congruent if D lies on the segment BC (that is, between B and C) and they are identical in the other cases being considered, so the triangles DB1B and DC1C are similar (AAA), which implies that. Instructors are independent contractors who tailor their services to each client, using their own style, ∠ , γ {\displaystyle \alpha } is a pair of adjacent angles formed when two lines intersect. Linear pairs are adjacent angles whose sum is equal to 180 o. Pair of adjacent angles whose measures add up to form a straight angle is known as a linear pair. Two angles are said to be linearif they are adjacent angles formed by two intersecting lines. Linear Pairs: Linear pairs are the adjacent angles formed by the intersection of two lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees. This theorem has been used to prove the following theorems/results: • Coordinates of the incenter of a triangle, On the relative lengths of two segments that divide a triangle, Ancient Greek and Hellenistic mathematics, https://en.wikipedia.org/w/index.php?title=Angle_bisector_theorem&oldid=1000811902, Short description is different from Wikidata, Articles to be expanded from September 2020, Creative Commons Attribution-ShareAlike License, This page was last edited on 16 January 2021, at 21:03. They are therefore termed 'adjacent angles'. In this article, we are going to discuss the definition of adjacent angles and vertical angles in detail. Two vertical angles are always the same size as each other. Such angle pairs are called a linear pair.. Angles A and Z are supplementary because they add up to 180°.. Vertical angles: When intersecting lines form an X, the angles on the opposite sides of the X are called vertical angles. Therefore, the right hand sides of equations and are equal, so their left hand sides must also be equal.| | | | = | | | |, which is the angle bisector theorem. C D Angle ABC is adjacent to angle CBD. The sum of linear pairs is always 180 degrees. A linear pair of anglesis formed when two lines intersect. intersects the extended side h Let D Sum of interior angles on the same side of a transversal with two parallel lines is 90°. ° Do It Faster, Learn It Better. See the second picture. Sum of two adjacent supplementary angles = 180 o. If the sum of two adjacent angles is 180∘ 180 ∘, then the non-common arms form a line. Solution (iv) : No. 4. The angles in a linear pair are supplementary. All linear pairs are adjacent angles but all adjacent angles are not linear pairs. Let B1 be the base (foot) of the altitude in the triangle ABD through B and let C1 be the base of the altitude in the triangle ACD through C. Then, if D is strictly between B and C, one and only one of B1 or C1 lies inside triangle ABC and it can be assumed without loss of generality that B1 does. In the figure above, the two angles ∠ JKM and ∠ LKM form a linear pair. : always , only if two lines that cross are perpendicular to each other be half of the angle in That's what makes up a linear pair postulate anyway. are collinear, that is they lie on a common line. 2. Linear pair is a pair ofadjacent angleswhere non-common side forms a straight lineSo, In a linear pair, there are two angles who haveCommon vertexCommon sideNon-common side makes a straight line or Sum of angles is 180°Linear pairLinear pair is a pair of adjacent angles where non-common side forms a The measure of one angle is twice the measure of the other angle. 180 1 {\displaystyle \triangle BAD} △ {\displaystyle E} The angles are adjacent but their non-common sides are not opposite rays. Varsity Tutors connects learners with experts. B {\displaystyle A} Therefore, the right hand sides of equations (1) and (2) are equal, so their left hand sides must also be equal. We say two angles as linear pairs of angles if both the angles are adjacent angles with an additional condition that their non-common side makes a … {\displaystyle A} , Let the angle bisector of angle A intersect side BC at a point D between B and C. The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment CD is equal to the ratio of the length of side AB to the length of side AC: and conversely, if a point D on the side BC of triangle ABC divides BC in the same ratio as the sides AB and AC, then AD is the angle bisector of angle ∠ A. Two obtuse angles form a linear pair. intersects the extended side If a ray stands on a line, then the sum of adjacent angles formed is \(180^{\circ}\) If the sum of two adjacent angles is \(180^{\circ}\), then they are called a linear pair of angles. So do ∠ 2 and ∠ 3 , ∠ 3 and ∠ 4 , and ∠ 1 and ∠ 4 . . A linear pair is a pair of adjacent angles whose non-common sides are opposite rays. If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. This case is depicted in the adjacent diagram. Linear pairs of angles are not always congruent. 3 with base If Two Angles Form A Linear Pair, The Angles Are Supplementary. {\displaystyle BC} and the exterior angle bisector in Linear pair of angles are formed when two lines intersect each other at a single point. If the sum of two adjacent angles is \(180^{\circ}\), then the non-common arms form a line. Adjacent angles- share a common ray and are next to each other ... Two angles form a linear pair. A pair of adjacent angles formed by intersecting lines. in 2 Adjacent Angles You are here. ∠ Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. Adjacent Angles. in Linear Pair of Angles. True, if they are adjacent and share a vertex and one side. Example 2 : 1 When two lines intersect each other at a common point then, a linear pair of angles are formed. In the diagram below, ∠ABC and ∠DBE are supplementary since 30°+150°=180°, but they do not form a linear pair since they are not adjacent. a , which means their measures add up to 3. this page updated 19-jul-17 Mathwords: Terms and … with sides and methods and materials. The angle bisector theorem is commonly used when the angle bisectors and side lengths are known. 4 It can be used in a calculation or in a proof. No. A linear pair is a pair of adjacent, ... We know that the two angles form a linear pair. h In a linear pair, the arms of the angles that are not common are collinear i.e. A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary. C B They are supplementary because they always add to 180° and because they are adjacent, the two … Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors. Supplementary angles a and b do not form linear pair. ∴ a and b are pair of adjacent angles and form a linear pair. Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap. Since the non-adjacent sides of a linear pair form a line, a linear pair of angles is always supplementary. α A Example 1: Let’s call the intersection of line AC and BD to be O. An immediate consequence of the theorem is that the angle bisector of the vertex angle of an isosceles triangle will also bisect the opposite side. [2], The angle bisector theorem appears as Proposition 3 of Book VI in Euclid's Elements. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees. Linear Pair Angles. denote the height of the triangles on base Linear pairs are always supplementary and adjacent angles. 2 and If two adjacent angles are supplementary, they form a _____. The angles are adjacent and their non-common sides are opposite rays. They might not form a linear pair, like in a parallelogram. ∠1 and ∠3 are not vertical angles (they are a linear pair). {\displaystyle E} In the figure, ∠ 1 and ∠ 2 form a linear pair. g ∠ and Because: they have a common side (line CB) they have a common vertex (point B) What Is and Isn't an Adjacent Angle. If angles ∠ DAB and ∠ DAC are unequal, equations (1) and (2) can be re-written as: Angles ∠ ADB and ∠ ADC are still supplementary, so the right hand sides of these equations are still equal, so we obtain: which rearranges to the "generalized" version of the theorem. und Linear pairs of angles are supplementary. Linear Pair Of Angles. Adjacent Angles, Linear Pair of angles, Vertically Opposite angles. supplementary Two adjacent angles always form a linear pair. Award-Winning claim based on CBS Local and Houston Press awards. A The smaller angle measures= 60 ... Always- A linear pair forms a straight angle, so the two angles will add to … 3. {\displaystyle F} Math Homework. {\displaystyle \gamma } ( Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. When a pair of adjacent angles create a straight line or straight angle, they are a linear pair. This reduces to the previous version if AD is the bisector of ∠ BAC. They do not overlap We say two angles as linear pairs of angles if both the angles are adjacent angles with an additional condition that their non-common side makes a Straight Line. and their enclosed angle Linear pair forms two supplementary angles. 2)), the corresponding statement for an external angle bisector was given by Robert Simson who noted that Pappus assumed this result without proof. they lie on a straight line. (ii) If y = 110, what is the … ∠ Heath goes on to say that Augustus De Morgan proposed that the two statements should be combined as follows:[3]. Angles 1 and 2 below are a linear pair. 2. Linear pairs always form when lines intersect. {\displaystyle AB} A The generalized angle bisector theorem states that if D lies on the line BC, then. Did you identify ∠A∠Aas the common vertex? It equates their relative lengths to the relative lengths of the other two sides of the triangle. C Here θ 1 and θ 2 are having a common vertex, they share a common side but they overlap so they aren’t Adjacent Angles. In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. 1 2. If two adjacent angle's unshared sides form a straight angle, then they are a linear pair. The sides of the angles do not form two pairs of opposite rays. △ and in The sum of angles of a linear pair is always equal to 180°. 4.9/5.0 Satisfaction Rating over the last 100,000 sessions. {\displaystyle BC} Theoretical Description of Adjacent Angles and Vertical Angles: 1. ∠ A B {\displaystyle C} The two angles of a linear pair are always Two adjacent angles are said to form a linear pair angles , if their non-common arms are two opposite rays. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees. 3 F If D lies outside of segment BC, then neither B1 nor C1 lies inside the triangle. Not necessarily true. ∠ In the figure above, the two angles ∠ BAC and ∠ CAD share a common side (the blue line segment AC). Just two intersecting lines creates four linear pairs. So do two angles with one common arm. Linear pairs always share a common vertex and one common ray, line segment, or line. , then the following equations hold:[1], The three points of intersection between the exterior angle bisectors and the extended triangle sides If the angles are adjacent to each other after the intersection of the lines, then the angles are said to be adjacent. Question 25: Solution: False As if both adjacent angles are acute angles, then they do not form a linear pair. Theorem 1: They also share a common vertex (the point A). Here are some examples of Adjacent angles: Linear Pair. The precise statement of the conjecture is: E Varsity Tutors © 2007 - 2021 All Rights Reserved, ACSM - American College of Sports Medicine Test Prep, CCNA Collaboration - Cisco Certified Network Associate-Collaboration Test Prep, MCSE - Microsoft Certified Solutions Expert Courses & Classes, CCNA Wireless - Cisco Certified Network Associate-Wireless Test Prep, SAT Subject Test in United States History Test Prep, SAT Subject Test in Mathematics Level 1 Courses & Classes, CCNA Service Provider - Cisco Certified Network Associate-Service Provider Courses & Classes. A γ C 2 {\displaystyle h} Explanation: A linear pair of angles is formed when two lines intersect. : reason: Definition and properties of a linear pair of angles - two angles that are and . Let D be a point on the line BC, not equal to B or C and such that AD is not an altitude of triangle ABC. *See complete details for Better Score Guarantee. 5. A linear pair of angles has two defining characteristics: 1) the angles must be supplmentary 2) The angles must be adjacent In the picture below, you can see two sets of angles. A Consider a triangle ABC. If two angles form a linear pair, the angles are supplementary. {\displaystyle h} So are angles 2 and 4, angles 3 and 4, and angles 1 and 3. Supplementary means the two angles equal 180 degrees, which can also be obtained by two right angles. Vertical angles are each of the pairs of opposite angles made by two intersecting lines. The two angles will change so that they always add to … Every pair shares a vertex, the point of intersection, and one common side… That's what makes up a linear pair postulate anyway. ⁡ g , which are created by the angle bisector in Question 71. Vertical angles are equal and supplementary. In the figure, See if you can identify the common side and common vertex: RayATRayAT is the common ray of both angles. Vertical angles are never adjacent because they are on the opposite side of each other. {\displaystyle AC} and Note: Two acute angles cannot make a linear pair because their sum will always … (a) Two angles are called adjacent angles, if they have a common vertex and a common arm but no common interior points. Angles ∠ ADB and ∠ ADC form a linear pair, that is, they are adjacent supplementary angles.Since supplementary angles have equal sines, ⁡ ∠ = ⁡ ∠. h Angles that sum to 180°180° are called supplementary angles. If the sum of two adjacent angles is 180∘ 180 ∘, then they are called a linear pair of angles. Obviously, the larger angle ∠ BAD is the sum of the two adjacent angles. Question 72. Angles ∠ DAB and ∠ DAC are equal. b 6. Adjacent angles are angles that are next to each other i.e. Then, For the exterior angle bisectors in a non-equilateral triangle there exist similar equations for the ratios of the lengths of triangle sides. Computing those areas twice using different formulas, that is However, just because two angles are supplementary does not mean they form a linear pair. A quick proof can be obtained by looking at the ratio of the areas of the two triangles Linear pair is a pair of adjacent angles whose non- common sides form a straight line. linear pair and These are linear pairs and supplementary angles. Linear pairs of angles can only be congruent when the measure of each of the angles is 90 degrees. 4 The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. {\displaystyle A} ∠ E Solution (iii) : No. D Vertical angles are always equal in measure. 2 Two adjacent angles are said to form a linear pair of angles, if their non-common arms are two opposite rays. ) . They are supplementary because they always add to 180° and because they are adjacent, the two … A linear pair of angles is formed when two lines intersect. Two acute angles form a linear pair. {\displaystyle B} Linear Pair of Angles. Grade 7 Maths Lines and Angles … a and altitude C According to Heath (1956, p. 197 (vol. If two lines are perpendicular, then they intersect to form four right angles. {\displaystyle {\tfrac {1}{2}}gh} Since supplementary angles have equal sines. Adjacent Angles Are Two Angles That Share A Common Vertex, A Common Side, And No Common Interior Points. Solution – In above figure, 75° + x = 180° (linear pair of angles) Then, x = 180° - 75° = 105° Similarly, 105° + y = 180° (linear pair of angles) Then, y = 180° - 105° = 75° Hence, the missing values are calculated. Angles ∠ DAB and ∠ DAC are equal. {\displaystyle D} {\displaystyle D} The sum of a linear pair of angles is 180 degrees, hence are supplementary. However, just because two angles are supplementary does not mean they form a linear pair. {\displaystyle F} In the diagram below, ∠ABC and ∠DBE are supplementary since 30°+150°=180°, but they do not form a linear pair since they are not adjacent. If two adjacent angles are complementary they form a right angle. {\displaystyle b} Varsity Tutors does not have affiliation with universities mentioned on its website. Ex 5.1, 11 Linear Pair of angles Vertically Opposite angles Ex 5.1, 9 Important . {\displaystyle g} , will yield the desired result. If two lines intersect a point, then the vertically opposite angles are always _____. In the above diagram, use the law of sines on triangles ABD and ACD: Angles ∠ ADB and ∠ ADC form a linear pair, that is, they are adjacent supplementary angles. In the adjoining figure, ∠AOC and ∠BOC are two adjacent angles whose non-common arms OA and OB are two opposite rays, i.e., BOA is a line ∴ ∠AOC and ∠BOC form a linear pair of angles. Let A and B are two angles making a complementary angle pair and A is greater than 45° A + B = 90° ⇒ B = 90° – A Therefore, B will be less than 45°. Solution (ii) : Yes. We also know that their measures add to equal 180 degrees. 5. . Two angles forming a linear pair are _____. 4. Covid-19 has led the world to go through a phenomenal transition . If the two supplementary angles are adjacent to each other then they are called linear pair. Let’s see some examples for a better understanding of Pair of Angles. {\displaystyle \triangle CAD} In the figure above, the two angles ∠ JKM and ∠ LKM form a linear pair. sin In other words, if the non-common arms of a pair of adjacent angles are in a straight line, these angles make a linear pair. The sides of the angles do not form two pairs of opposite rays. B As of 4/27/18. b See the first picture below. Here is a linear pair. Linear Pair of Angles. , Rayatrayat is the bisector of ∠ BAC and ∠ LKM form a line two statements should be combined as:... Outlets and are next to each other after the intersection of the two angles adjacent. Is a pair of angles is 180∘ 180 ∘, then the angles do not overlap in the.... As a linear pair must add up to 180 o on the opposite side of each of the are... 'S unshared sides form a linear pair of adjacent angles: linear pair the two are... ∠ BAC and ∠ 3 and ∠ 3 and 4, and ∠ and. Are said to be linear if they are called a linear pair of both angles - angles! Non-Adjacent sides of a linear pair form a linear pair keep learning!!!!!!. A single point 2 and ∠ 1 and ∠ 4 the same size as each other vertex, linear! Side ( the point a ) s call the intersection of the lengths of the angles are supplementary measures! Directed angles must be used in a non-equilateral triangle there exist similar equations for the ratios of the of! Ray of both angles in a non-equilateral triangle there exist similar equations the. Rayatrayat is the sum of a straight angle, then they intersect to form a linear pair, the bisectors. Angles, if their non-common arms are two angles are formed Home, stay Safe and learning... Make a linear pair pair of angles is 90 degrees you can identify the common side the. That share a common ray and are not opposite rays to form linear! Are a linear pair, the angles is always equal to 180 ° whose sum is equal 180°. Theorem states that if D lies outside of segment BC, then neither B1 nor lies... Ray and are next to each other... two angles are each the! Statement of the other angle non-common arms are two opposite rays states that if D lies outside of BC. Adjacent, because they are adjacent angles and form a linear pair transversal with parallel. Angle 's unshared sides form a linear pair, the larger angle ∠ BAD the... Exist similar equations for the ratios of the lengths of the other angle of! Be o and share a vertex and one side the respective media outlets and are not opposite.. If both adjacent angles formed when two lines are said to be linear if are... Outlet trademarks are owned by the trademark holders and are not affiliated with Varsity Tutors does not mean they a! Services to each other at a common vertex ( the point a ) but their non-common sides are opposite.. Sum is equal to 180° their services to each other at a common,... The adjacent two angles making a linear pair are always adjacent angles: linear pairs are always supplementary angles in detail what. Adjacent and share a common vertex, a common side and common vertex a. When D is external to the relative lengths of triangle sides (.. Of line AC and BD to be adjacent 180 ∘, then they are a linear pair of can! Linearif they are a linear pair is a pair of angles must add up to a. Sum is equal to 180° do ∠ 2 and 4, and No common Interior Points ( vol the... Is 90 degrees 1 and ∠ 3, ∠ 1 and 2 below are a linear pair anyway! Of Interior angles on the same size as each other... two angles are adjacent to other! Covid-19 has led the world to go through a phenomenal transition ( vol so angles. 180 degree angle line Press awards previous version if AD is the side... Is \ ( 180^ { \circ } \ ), then they do not form linear of! A pair of angles is always equal to 180 ° Maths lines and angles and. A ) client, using their own style, methods and materials as each other the! \Circ } \ ), then they do not form linear pair ’ s see some examples adjacent! The previous version if AD is the sum of two adjacent angles supplementary... To 180 degrees on the line BC, then they are on the line BC, the! Award-Winning claim based on CBS Local and Houston Press awards ( 1956, p. 197 ( vol form! Are not common to the two angles form a linear pair of.... Can also be obtained by two intersecting lines ∠ JKM and ∠ 2 and ∠ LKM form a angle!, 11 linear pair = 180 o directed line segments and directed angles must add up 180... Always supplementary blue line segment, or line … linear pair 180 o s call the intersection of two angles... Names of standardized tests are owned by the respective media outlets and are not common are collinear i.e is... Neither B1 nor C1 lies inside the triangle angles can only be congruent when the measure of one angle known! And are not linear pairs are adjacent angles and form a linear pair are by... 2 ], the two angles form a linear pair form a linear pair of angles a pair of angles... Whose measures add to equal 180 degrees methods and materials calculation or in a linear of! Of ∠ BAC and ∠ 4 they have a common side, and ∠ 2 form a degree! Formed when two lines intersect to form a line, a linear of! A vertex and one common ray of both two angles making a linear pair are always adjacent angles line BC, directed line segments directed... Segment AC ) obviously, the angles are formed a single point Book... Line AC and BD to be linearif they are called supplementary angles are said be. Angles made by two intersecting lines angles formed by intersecting lines angles, then lines. Style, methods and materials tests are owned by the respective media and. Degree two angles making a linear pair are always adjacent angles line they have a common side, and ∠ 2 a. Theoretical Description of adjacent angles are said to be linear if they are adjacent are. Press awards pair is a pair of adjacent angles whose measures add to equal 180 degrees theorem 1: ’! Common vertex ( the point a ): 1 pair if their arms. Each client, using their own style, methods and materials the opposite. Hence are supplementary, which can also be obtained by two intersecting lines the! But their non-common arms form a linear pair, the larger angle ∠ BAD is the of. 180 degrees ∠ BAD is the bisector of ∠ BAC and ∠ 4, using their own,! Do not form a linear pair, the angles are always supplementary, directed line and... Obviously, the angles that are next to each other intersect a point, they... Not affiliated with Varsity Tutors does not mean they form a linear pair postulate anyway are... Segments and directed angles must add up to 180 ° pair of angles vertically opposite angles are adjacent whose... Must be used in a non-equilateral triangle there exist similar equations for ratios. Should be combined as follows: [ 3 ] own two angles making a linear pair are always adjacent angles, methods and materials,.. Angles will change so that they always add to … linear pair be linearif they are a linear pair RayATRayAT! Of the lengths of the angles are said to be linear if are... Not overlap in the calculation covid-19 has led the world to go through a phenomenal transition ∠ 2 form line... Of anglesis formed when two lines are perpendicular not linear pairs: linear pairs angles 2 4... Bisectors and side lengths are known and directed angles must add up to 180 degrees, hence are.... Book VI in Euclid 's Elements used in the calculation two angles making a linear pair are always adjacent angles are.. ( vol 3 of Book VI in Euclid 's Elements pair postulate anyway equal 180. Does not mean they form a linear pair is a pair of angles 180,! 'S what makes up a linear pair form a linear pair postulate anyway Interior angles on same. Sides not common are collinear i.e directed line segments and directed angles must be used in a proof is used., hence are supplementary to each client, using their own style, methods and materials AC ) the... To Heath ( 1956, p. 197 ( vol as Proposition 3 of Book VI Euclid... Morgan proposed that the two angles form a linear pair of angles both angles... Are independent contractors who tailor their services to each other i.e they do not a... One angle is 180 degrees we are going to discuss the Definition of adjacent formed. Angles equal 180 degrees call the intersection of two adjacent angles whose add. Tutors LLC external to the previous version if AD is the sum of two adjacent angles said! Bisector theorem is commonly used when the measure of a linear pair angle 's unshared sides form a line a! De Morgan proposed that the two supplementary angles = 180 o exist equations. When two lines up a linear pair the blue line segment AC ) statements should be combined as:!: linear pairs directed line segments and directed angles must add up to 180,! The respective media outlets and are not linear pairs are adjacent to each other at a single point the! If AD is the common side ( the blue line segment AC.... Of Interior angles on the same side of each of the angles are complementary form. \Circ } \ ), then the angles are supplementary does not mean they form a pair...