<a and <b are complementary angles. The measure of <a is four times as big as <b. What is the measure of <a

Answer = 72°

Complementary angles always add up to be 90.
We can write the smaller angle as x and the bigger angle as 4x, because it is 4 times bigger than x.

x + 4x = 90
5x = 90
x = 18.

This proves the smaller angle, or angle B, is 18. We know angle A is 4 times as big as 18, so we can multiply 18 x 4 to get 72.

Double check = 72 + 18 = 90