# 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?

Sep 9, 2015

The first angle measures ${40}^{\circ}$ and the second angle measures ${50}^{\circ}$.

#### Explanation:

Two angles a re said to be complemetary angles when they add up to give an angle of ${90}^{\circ}$.

Let's assume that $\angle X$ is the first angle and $\angle Y$ is the second angle. You know that

$X + Y = {90}^{\circ}$

Moreover, you know that if you add the first angle to half of the second angle, you get an angle of ${65}^{\circ}$. This means that you can write

$X + \frac{1}{2} \cdot Y = {65}^{\circ}$

Use the first equation to find $X$ as a function of $Y$

$X = 90 - Y$

Plug this into the second equation to find $Y$

$90 - Y + \frac{1}{2} Y = 65$

$- \frac{1}{2} Y = 65 - 90$

$Y = 2 \cdot 25 = \textcolor{g r e e n}{{50}^{\circ}}$

This means that angle $X$ is

$X = 90 - \left(50\right) = \textcolor{g r e e n}{{40}^{\circ}}$