Two Angles Are Complementary.The Smaller Angle Is 15\Xb0less Than One Half The Measure Of The Larger Angle.What Are The Measures Of The Angles ?

Two angles are complementary.The smaller angle is 15°less than one half the measure of the larger angle.What are the measures of the angles ?

 

Answer:

20° (smaller angle)

70° (larger angle)

Step-by-step explanation:

Two angles are complementary.The smaller angle is 15°less than one half the measure of the larger angle.What are the measures of the angles ?

let x be the measure of the smaller angle

    y be the measure of the larger angle

x + y = 90°      (since they are complementary angles) ---- eq 1

x = (1/2)(y) - 15°                                                                  ---- eq 2

substitute eq 2 to eq 1

(1/2)(y) - 15° + y = 90°

solve for y

1.5y = 105°

y = 70° (larger angle)

x = (1/2)(y) - 15° = (1/2)(70°) - 15° = 20° (smaller angle)