Question

The measure of two complementary angles are in the ratio 1:4. What are the degree measures of the two angles

Answer 1

complementary means add up both angles to 90 degrees
let the first angle is a = x and the other is b = 4x (see that a : b = 1 : 4)

now take an equation :
a + b = 90
x + 4x = 90
5x = 90
x = 90/5
x = 18

so, a = x = 18 and
b = 4x = 4(18) = 72