7-2 Complementary and Supplementary Angles. Identify the pair of angles as complementary, supplementary, or neither. 1. ANSWER: neither ANSWER:
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1 Identify the pair of angles as complementary,, or neither A and B are complementary angles. The measure of B is (4x), and the measure of A is 50. What is the value of x? 10 neither 7. A skateboard ramp forms a 42º angle as shown. Find the value of x Use the figure below to name the following. Find the measure of x in the figure. 8. a pair of angles Sample answer: IJK, KJG a pair of complementary angles Sample answer: CGK, KGJ 10. a pair of vertical angles Sample answer: AKB, JKG esolutions Manual - Powered by Cognero Page 1
2 11. Use the figure below. a. Are 1 and 2 vertical angles, adjacent angles, or neither? 2 and 3? 1 and 3? b. Write an equation representing the sum of m 1 and m 2. Then write an equation representing the sum of m 2 and m Persevere with Problems Find the measure of each angle in the given situation. a. complementary angles E and F, where m E = (x 10)º and m F = (x + 2)º b. angles B and C, where m B = (2x 40)º and m C = (2x + 20)º a. m E = 39º, m F = 51º b. m B = 60º, m C = 120º 14. Persevere with Problems In the figure below, the sum of the measures of YXZ and WXV is 75. What is the measure of ZXW? c. Solve the equations you wrote in part b for m 1 and m 3, respectively. What do you notice? d. Make a Conjecture Use your answer from part c to make a conjecture as to the relationship between vertical angles. a. adjacent; adjacent; vertical b. m 1 + m 2 = 180 ; m 2 + m 3 = 180 c. m 1 = 180 m 2; m 3 = 180 m 2; Sample answer: m 1 and m 3 are equal. d. Sample answer: Vertical angles are congruent. 12. Reason Inductively When a basketball hits a hard, level surface, it bounces off at the same angle at which it hits. Use the figure to find the angle at which the ball hit the floor. 105º 15. Reason Inductively Is the statement below always, sometimes, or never true? Explain. If two angles are right angles, they must be. Sample answer: Right angles have a measure of 90, so two right angles will always have a sum of 180. this is the definition of angles. Identify the pair of angles as complementary,, or neither complementary esolutions Manual - Powered by Cognero Page 2
3 Multiple Representations Line a passes through (1, 4) and ( 4, 1). Line b passes through ( 3, 4) and (2, 1). neither 19. J and K are. The measure of J is (9x) and the measure of K is 45. What is the value of x? C and D are complementary. The measure of C is (4x) and the measure of D is 26. What is the value of x? 16 Identify Structure Determine whether the statement is always, sometimes, or never true. Explain your reasoning. 21. Two obtuse angles are. never; Sample answer: Since an obtuse angle is greater than 90, the sum of two obtuse angles must be greater than, not equal to, 180. a. Graphs Graph each line on the same coordinate plane. b. Words Describe the lines. c. Numbers What is the slope of each line? a. 22. Two vertical angles are complementary. sometimes; Sample answer: If the measure of each angle is 45, then the two angles are complementary. b. The lines appear to be perpendicular. c. line a: 1; line b: 1 esolutions Manual - Powered by Cognero Page 3
4 24. Which angle pairs below are? Select all that apply. 25. The angle at which the light ray hits the water is equal to the angle at which the light is reflected from the water. Select values to complete the equation below to find the value of x. What is the measure of the angle at which the light ray hits the water? What is the measure of the angle in degrees at which the light is reflected from the water? ; 45 ; 45 esolutions Manual - Powered by Cognero Page 4
5 Graph the figure with the given vertices on the coordinate plane. Then classify the figure. 26. Vertices: (1, 3), (1, 6), (5, 5), and (5, 3) 27. Vertices: (1, 2), (5, 2), (5, 6), and (1, 6) square trapezoid esolutions Manual - Powered by Cognero Page 5
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