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1-5 Angle Relationships Name an angle or angle pair that satisfies each condition. 8. two adjacent angles SOLUTION: Sample answer: Adjacent angles are two angles that lie in the same plane and have a common vertex and a common side. There are many adjacent angles in the figure. and are adjacent angles, and are adjacent angles. 90, then they are complementary adjacent angles. and share a common side and vertex, also . So, and are complementary adjacent angles. 12. two complementary nonadjacent angles SOLUTION: If the sum of the measures of two nonadjacent angles is 90, then they are complementary nonadjacent angles. and are nonadjacent angles, and . So, and are complementary nonadjacent angles. 13. two supplementary adjacent angles SOLUTION: 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. 9. two acute vertical angles SOLUTION: 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. 14. a linear pair whose vertex is F SOLUTION: Sample answer: A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays. and are linear pair with vertex F, and are linear pair with vertex F. 10. two obtuse vertical angles SOLUTION: Sample answer: Vertical angles are two nonadjacent angles formed by two intersecting lines. Nonadjacent angles HGE and FGD are formed by and intersecting at G. Each angle is greater than a right angle. Therefore, ∠HGE and ∠FGD are obtuse vertical angles. 11. two complementary adjacent angles SOLUTION: If the sum of the measures of two adjacent angles is 90, then they are complementary adjacent angles. and share a common side and vertex, also . So, and are complementary adjacent angles. 12. two complementary nonadjacent angles SOLUTION: eSolutions by Cognero If theManual sum -ofPowered the measures of two nonadjacent angles is 90, then they are complementary nonadjacent angles. 15. an angle complementary to FDG SOLUTION: Complementary angles are two angles with measures that have a sum of 90. Since is complementary to 16. an angle supplementary to CBF SOLUTION: Sample answer: Supplementary angles are two angles with measures that have a sum of 180. Since is supplementary to 17. an angle supplementary to JAE SOLUTION: Supplementary angles are two angles with measures that have a sum of 180. Since , is Page 1 supplementary to . 18. CCSS REASONING You are using a compass to SOLUTION: Sample answer: Supplementary angles are two angles with measures that have a sum of 180. Since Relationships is 1-5 Angle supplementary to 17. an angle supplementary to JAE SOLUTION: Supplementary angles are two angles with measures that have a sum of 180. Since , is supplementary to . 20. SOLUTION: The angles in a linear pair are supplementary. So, . 18. CCSS REASONING You are using a compass to drive 23° east of north. Express your direction in another way using an acute angle and two of the four directions: north, south, east, and west. Explain your reasoning. So, x is 12. SOLUTION: Since the measure of the angle between north and east is 90, you can use the complement of (the original angle) and describe the direction as north of east instead of east of north. The complement of is . So, the answer is north of east. 21. SOLUTION: Since (2x + 25)° and (3x – 10)° are vertical angles, they are congruent. Find the value of each variable. 19. SOLUTION: In the figure, the angle and the angle are vertical angles. Vertical angles are congruent. Solve for y. eSolutions Manual - Powered by Cognero 20. SOLUTION: Page 2 22. SOLUTION: So, the values of the variables are x = 46 and y = 18. Solve for y. 1-5 Angle Relationships 23. SOLUTION: Supplementary angles have measures that sum to 180. So, and . 22. SOLUTION: In the figure, angle and are vertical angles. Vertical angles are congruent. So, . angle Consider . The angles in a linear pair are supplementary. So, 24. So, the values of the variables are x = 46 and y = 18. SOLUTION: In the figure, angle and vertical angles. Vertical angles are congruent. So, angle are . 23. SOLUTION: Supplementary angles have measures that sum to 180. So, and . In the figure, . Consider eSolutions Manual - Powered by Cognero . Page 3 1-5 Angle Relationships 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. 24. SOLUTION: In the figure, angle and vertical angles. Vertical angles are congruent. So, SOLUTION: Supplementary angles are two angles with measures that have a sum of 180. Then, . It is given that . angle are . Substitute. Substitute In the figure, in . . 26. ALGEBRA The measure of an angle’s supplement is 76 less than the measure of the angle. Find the measure of the angle and its supplement. SOLUTION: Supplementary angles are two angles with measures that have a sum of 180. Let x and y be the angle and its supplement respectively. 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. SOLUTION: Supplementary angles are two angles with measures that have a sum of 180. Then, . It is given that . By the definition of supplementary angles, . Substitute. Substitute Substitute in . eSolutions Manual - Powered by Cognero 26. ALGEBRA The measure of an angle’s supplement is 76 less than the measure of the angle. Find the in . The measure of the angle and its supplement are 128 and 52 respectively. 27. ALGEBRA The measure of the supplement of an angle is 40 more than two times the measure of the Page 4 complement of the angle. Find the measure of the angle. 1-5 Angle Relationships The measure of the angle and its supplement are 128 and 52 respectively. 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. SOLUTION: 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 The measure of an angle is 40. 28. ALGEBRA 3 and 4 form a linear pair. The measure of 3 is four more than three times the measure of 4. Find the measure of each angle. SOLUTION: The angles in a linear pair are supplementary. So, . It is given that . Substitute in eSolutions Manual - Powered by Cognero . Page 5