154 Chapter 2 Linear Equations and Inequalities 49. Sometimes memory devices are helpful for remembering mathematical facts. Recall that the sum of two complementary angles is .That is, two complementary angles when added together form a right angle or “corner.”The words Complementary and Corner both start with the letter “C.” Derive your own memory device for remembering that the sum of two supplementary angles is 180°. y y° x x y 90 50. Two angles are complementary. One angle is less than the other angle. Find the measures of the angles. 52. Two angles are supplementary. One angle is three times as large as the other angle. Find the measures of the angles. 54. Refer to the figure.The angles, a and b, are vertical angles. 57. The largest angle in a triangle is three times the smallest angle.The middle angle is two times the smallest angle. Given that the sum of the angles in a triangle is 180° , find the measure of each angle. (See Example 5.) x° x° y° 180° a (3y 26) 4° b 58. The smallest angle in a triangle measures less than the largest angle.The middle angle measures 60° less than the largest angle. Find the measure of each angle. 90° 59. The smallest angle in a triangle is half the largest angle.The middle angle measures 30° less than the largest angle. Find the measure of each angle. 60. The largest angle of a triangle is three times the middle angle.The smallest angle measures 10° less than the middle angle. Find the measure of each angle. 90° Complementary angles form a “Corner” Supplementary angles . . . (5y 54) (3x)° (2x)° x° x° (2x 3)° (x 17)° 20° 51. Two angles are complementary. One angle is less than three times the other angle. Find the measures of the angles. (See Example 4.) 53. Two angles are supplementary. One angle is more than four times the other. Find the measures of the two angles. 6° 55. Find the measures of the vertical angles labeled in the figure by first solving for x. 56. Find the measures of the vertical angles labeled in the figure by first solving for y. a. If the measure of is 32°, what is the measure of b. What is the measure of the supplement of a? a b? Figure for Exercise 54
miller_beginning_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above