1-5 Angle Relationships. Name an angle pair that satisfies each condition.
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1 Name an angle pair that satisfies each condition 1 two acute vertical angles Vertical angles are two nonadjacent angles formed by two intersecting lines You can use the corner of a piece of paper to see that ZVY and WVU are less than right angles Therefore, and are acute vertical angles 13 two supplementary adjacent angles Sample answer: If the sum of the measures of two adjacent angles is 180, then they are supplementary adjacent angles There are many supplementary adjacent angles in the figure and share a common side and vertex, also So, and are supplementary adjacent angles 15 an angle complementary to FDG Complementary angles are two angles with measures that have a sum of 90 Since is complementary to 17 an angle supplementary to JAE Supplementary angles are two angles with measures that have a sum of 180 Since, is supplementary to Find the value of each variable Name an angle or angle pair that satisfies each condition 19 In the figure, the angle and the angle are vertical angles Vertical angles are congruent 9 two acute vertical angles Sample answer: Vertical angles are two nonadjacent angles formed by two intersecting lines There are many acute vertical angles in the figure and are acute vertical angles esolutions Manual - Powered by Cognero Page 1
2 21 Since (2x + 25) and (3x 10) are vertical angles, they are congruent 23 Supplementary angles have measures that sum to 180 So, and Consider Solve for y 25 ALGEBRA E and F are supplementary The measure of E is 54 more than the measure of F Find the measures of each angle Supplementary angles are two angles with measures that have a sum of 180 Then, It is given that Substitute Substitute in esolutions Manual - Powered by Cognero Page 2
3 27 ALGEBRA The measure of the supplement of an angle is 40 more than two times the measure of the complement of the angle Find the measure of the angle Let x be the measure of an angle The measure of an angle which is complementary to angle is The measure of an angle which is supplementary to angle is 31 If m LNM = 8x + 12 and m JNL = 12x 32, find m JNP The angles in a linear pair are supplementary So, and are vertical angles Since the vertical angles are congruent, The measure of an angle is 40 ALGEBRA Use the figure below Substitute So, in 29 If m KNL = 6x 4 and m LNM = 4x + 24, find the value of x so that KNM is a right angle In the figure, Since is a right angle, esolutions Manual - Powered by Cognero Page 3
4 33 PHYSICS As a ray of light meets a mirror, the light is reflected The angle at which the light strikes the mirror is the angle of incidence The angle at which the light is reflected is the angle of reflection The angle of incidence and the angle of reflection are congruent In the diagram below, if m RMI = 106, find the angle of reflection and m RMJ 35 ALGEBRA and intersect at point V If m WVY = 4a + 58 and m XVY = 2b 18, find the values of a and b so that is perpendicular to Since and intersect at point V and is perpendicular to, and The angle of reflection and the angle of incidence are congruent So, In the figure, Substitute The angle of reflection measures 53 In the figure, So, a is 8 and b is 54 esolutions Manual - Powered by Cognero Page 4
5 Determine whether each statement can be assumed from the figure Explain 37 4 and 8 are supplementary Since and form a linear pair, they are supplementary The answer is Yes 39 From the figure, 3 and 6 are adjacent Since 5 is a right angle, 3 and 6 will be complementary This determines that both angles are acute However, unless we know that the larger angle was bisected to form 3 and 6, the measures of and are unknown So, we cannot say The answer is No 41 5 and 7 form a linear pair A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays and do not form a linear pair, since they are not adjacent angles 49 JUSTIFY ARGUMENTS Are there angles that do not have a complement? Explain Complementary angles are two angles with measures that have a sum of 90 By definition, the measure of an angle must be greater than 0 So, each angle must have a measure less than 90 Thus, each angle in a complementary pair is an acute angle Angles that have a measure greater than or equal to 90 can not have a complement, since the addition of any other angle measure will produce a sum greater than 90 Therefore, right angles and obtuse angles do not have a complement esolutions Manual - Powered by Cognero Page 5
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2 and 6 4 and 8 1 and 5 3 and 7
Geo Ch 3 Angles formed by Lines Parallel lines are two coplanar lines that do not intersect. Skew lines are that are not coplanar and do not intersect. Transversal is a line that two or more lines at different