1.6 Start Thinking. 1.6 Warm Up. 1.6 Cumulative Review Warm Up

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1 .6 Start Thinking In Section.5, you learned that a straight angle is an angle with a measure of 0. Imagine the straight angle you are measuring is the x-axis of a coordinate plane and the origin is the center of the angle. If you pull down the negative x-axis side so that it is in Quadrant III, how could you find the measure of the angle going counterclockwise?.6 Warm Up Solve.. 4x 0 =. 7 = c 4. = 9x 4. 7 = 5n + 5 4n 5. x + + = x 5 6. x x + 7 = x.6 umulative Review Warm Up Write the sentence as an equation and solve.. The difference between a number and 4 is.. Twice the difference between 5 times a number and 6 is.. Fourteen is 7 times the difference between a number and. 4. Four consecutive odd integers such that times the last integer is 5 more than the sum of the first integers. opyright Big Ideas Learning, LL 9

2 Name ate.6 Practice In Exercises, use the figures.. Name a pair of adjacent complementary angles.. Name a pair of nonadjacent complementary angles.. Name a pair of nonadjacent supplementary angles. In Exercises 4 and 5, find the angle measure. 4. is a complement of, and m = 6. Find m. 5. is a supplement of 4, and m 4 = 75. Find m. B 5 F G 55 5 H 67 E J In Exercises 6 and 7, find the measure of each angle. 6. WXY and YXZ are supplementary angles, m WXY = 6x + 59 ), and x ) m YXZ = B and B are complementary angles, m B = x + 6 ), and x ) m B = 4 4. In Exercises 0, use the figure.. Identify the linear pairs that include re and 5 vertical angles? Explain your reasoning. 0. re and 4 vertical angles? Explain your reasoning. 5 4 In Exercises, write and solve an algebraic equation to find the measure of each angle based on the given description.. Two angles form a linear pair. The measure of one angle is 4 more than the measure of the other angle.. The measure of an angle is three times the measurement of its complement.. The measure of one angle is 5 less than half the measurement of its supplement. 4. The figure shows the design on an outdoor fence. a. Name a pair of adjacent supplementary angles. b. Name a pair of nonadjacent supplementary angles. c. Identify the linear pairs that include 5. d. Find m. Explain your reasoning opyright Big Ideas Learning, LL

3 Name ate.6 Practice B In Exercises, use the figures.. Name a pair of adjacent complementary angles.. Name a pair of nonadjacent complementary angles.. Name a pair of nonadjacent supplementary angles. 4 B 56 E 4 G H 6 4 J F K In Exercises 4 and 5, find the angle measure. 4. is a complement of, and m = 7. Find m. 5. is a supplement of 4, and m 4 = 6.7. Find m. In Exercises 6 and 7, find the measure of each angle. 6. B and B are supplementary angles, m B = 7x and m B = x. 7. WXY and YXZ are complementary angles, m WXY = x + 5 ), and m YXZ x ) = 5. In Exercises, use the figure.. Identify the linear pairs) that include. 9. Identify the linear pairs) that include. 0. re 6 and vertical angles? Explain your reasoning.. re 7 and 9 vertical angles? Explain your reasoning In Exercises 4, write and solve an algebraic equation to find the measure of each angle based on the given description.. The measure of an angle is 9 more than twice its complement.. Two angles form a linear pair. The measure of one angle is four times the measure of the other angle. 4. Two angles form a linear pair. The measure of one angle is 5 more than the measure of the other angle. In Exercises 5 and 6, tell whether the statement is always, sometimes, or never true. Explain your reasoning. 5. The sum of the measures of a linear pair of angles is The sum of the measures of a pair of vertical angles is 0. opyright Big Ideas Learning, LL

4 Name ate.6 Enrichment and Extension omplementary and Supplementary ngles radian is a standard unit of measure used to measure angles. The conversion from degrees to radians is 0 = π radians. Example : onvert the sum of complementary and supplementary angles into radians. Solution: π radians π 90 = radians 0 π radians 0 = π radians 0 omplementary angles sum to π radians. Supplementary angles sum to π radians. Example : etermine if the two angles are complementary, supplementary, or neither: π π and 4 Solution: π π = 4 π π 5π + = Multiply by an identity to get the L. dd the two measurements. The sum of 5 π π does not equal or π, so the final answer is neither. etermine if the two angles are complementary, supplementary, or neither. π 4π π π 5π 5π.,.,., π 7π, π π 5., π π, 5 0 If possible, find the angle complementary and supplementary to the given angle. 7. π 5. π 4 9. π 7 0. π 5. 7π 4. 7π opyright Big Ideas Learning, LL

5 Name ate.6 Puzzle Time Why id The Student Eat His Math Exam? B E F G H I J omplete each exercise. Find the answer in the answer column. Write the word under the answer in the box containing the exercise letter. 5 NOTES 5 KEYS 4 BEUSE 6 THE 6 PIEE 4 OOR 7 WS KE THE Find the angle measure.. is a complement of and m = 49. Find m. B. is a supplement of 4 and m = 9. Find m and 6 are vertical angles and m 5 =. Find m and are linear angles and m 7 is 4 times that of m. Find m. E. is a supplement of and m =. Find m. F. is a complement of 4 and m =. Find m 4. G. Find m B. H. Find m B. x + 0 x 0) X I. Find m XYW. J. Find m WYZ. B W x x + 0 Y Z 6 SI 4 SME 40 OF 9 LLE 65 GOT TEHER 4 SHE 6 RE 49 IT 7 HER opyright Big Ideas Learning, LL