# Question #827f6

Jun 12, 2016

Largest angle: ${100}^{\circ}$

#### Explanation:

If the measure of the smallest angle is $a$
then the other two angles (given the $1 : 3 : 5$ ratio)
would be $3 a$ and $5 a$

We know that the sum of the angles of a triangle is ${180}^{\circ}$
So
$\textcolor{w h i t e}{\text{XXX}} a + 3 a + 5 a = {180}^{\circ}$
$\Rightarrow$
$\textcolor{w h i t e}{\text{XXX}} 9 a = {180}^{\circ}$

$\textcolor{w h i t e}{\text{XXX}} a = {20}^{\circ}$

Since the largest angle is $5 a$
the largest angle is $5 \times {20}^{\circ} = {100}^{\circ}$