# The angles of a triangle are in the ratio 3:4:5. What is the measure of the smallest angle?

Apr 30, 2018

45 is the smallest angle in your triangle.

#### Explanation:

The sum of the interior angles of a triangle will be 180°.

Therefore, think of the ratios of 3:4:5 as variables followed by "x" (3x, 4x, and 5x).

Combine like terms and set the equation equal to 180, the amt. of degrees in a triangle:

123$x$ = 180

Now, divide to isolate for $x$:

$\left(\frac{180}{12}\right)$ = 15 , so $x$ = 15

Now, substitute x for 15 in your variables:

3$x$, 4$x$, and 5$x$
3(15), 4(15), and 5(15)
45, 60, and 75 = 180

Therefore, 45 is the smallest angle.