The ratio of two complementary angles is 15: 30. what is the measure of the smaller angle?

75 degrees

Step-by-step explanation:

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

looks good.

the angles measure 15 degrees and 75 degrees.