# The measures of two angles have a sum of 90degrees. The measures of the angles are in a ratio of 2:1, how do you determine the measures of both angles?

Dec 1, 2016

The smaller angle is 30 degrees and the second angle being twice as large is 60 degrees.

#### Explanation:

Let's call the smaller angle $a$.

Because the ratio of the angles is $2 : 1$ the second, or larger angle is:

$2 \cdot a$.

And we know the sum of these two angles is 90 so we can write:

$a + 2 a = 90$

$\left(1 + 2\right) a = 90$

$3 a = 90$

$\frac{3 a}{3} = \frac{90}{3}$

$a = 30$