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

B

Answer 2

can you explain ?

Answer 3

if the angles are complementary, then their sum is 90 degrees.
let x = one of the angles and let y = the other.
you get:
x + y = 90
one of the angles is in the ratio of 1:5 with the other angle.
let x be that angle.
ratio formula says x/y = 1/5
solve for x to get x = (1/5)*y
replace y in the formula of x + y = 90 to get:
(1/5)*y + y = 90

combine like terms to get (6/5)*y = 90
multiply both sides of equation by (5/6) to get:
y = (5/6) * 90 = 75 degrees.
since x + y = 90, then x must be 15 degrees.
x = 15
y = 75
x/y = 15/75 = 1/5

Answer 4

wow ok thank you