# The measures of the triangle are in the ratio 2:4:6. What are the measures of the angles?

Dec 15, 2016

The measures of the angles are 30, 60 and 90 degrees.

#### Explanation:

I assume the question should read "the measures of the ANGLES of the triangle are in the ratio 2:4:6.

If the angles are in the proportion 2:4:6, the measures of the angles have the same scale factor $x$. And, the sum of the measures of the angles of a triangle is $180$.

$\implies 2 x + 4 x + 6 x = 180$

$12 x = 180$

$\frac{12 x}{12} = \frac{180}{12}$

$x = 15$

The measures of the angles are:

$2 x = 2 \left(15\right) = 30$
$4 x = 4 \left(15\right) = 60$
$6 x = 6 \left(15\right) = 90$