# Two angles are complementary. The sum of the measures of first angle and half the measure of the second angle is 65°. How do you find the measures of the angles?

##### 1 Answer

Sep 9, 2015

The first angle measures

#### Explanation:

Two angles a re said to be *complemetary angles* when they add up to give an angle of

Let's assume that

#X + Y = 90^@#

Moreover, you know that if you add the first angle to **half** of the second angle, you get an angle of

#X + 1/2 * Y = 65^@#

Use the first equation to find

#X = 90 - Y#

Plug this into the second equation to find

#90-Y + 1/2 Y = 65#

#-1/2Y = 65 - 90#

#Y = 2 * 25 = color(green)(50^@)#

This means that angle

#X = 90 - (50) = color(green)(40^@)#