Question

PLEASE HELP!! the measures of two complementary angles are in the ratio 2:3. What is the measure of the smaller angle?

Answer 1

The answer is 36°.

Complementary angles are those angles whose sum is 90°.

Let angles be x and y.
x + y = 90°
x : y = 2 : 3
_____
3 * x = 2 * y
3x = 2y
x + y = 90°
_____
x = 2/3*y
x + y = 90°
2/3y + y = 90°
2/3y + 3/3y = 90°
5/3y = 90°
5y = 90° * 3
5y = 270°
y = 54°

x + 54° = 90° 
x = 90° - 54°
x = 36°

The smaller angle is 36°

Answer 2

I hope this helps you