Question

The measure of two complementary angles are in the ratio 1 : 5. What are the degree measures of the two angles? What is the solution of each proportion?

A. 36° and 144°

B. 15° and 75°

C. 30° and 150°

D. 18° and 72°

Answer 1

If two angles are complementary then:
α + β = 90°
and because of the ratio: β = 5 α
α + 5 α = 90°
6 α = 90°
α = 90° : 6 = 15°
β = 5 · 15° = 75°
Answer: B ) 15° and 70°