Question

Find the measure of each angle.

The measures of the angles of an isosceles triangle are in the ratio $3:3:2$.

Short answer

The measure of each angle is,$67.5°$ ,$67.5°$ and$45°$

Step-by-step solution

Step 1. Given Information.

The ratio between angles of an isosceles triangle is,

$3:3:2$

Step 2. Concept Used.

The sum of angles of a triangle is,${180}^{\circ }$ .

Since,

ratio of the angles is always in the simplified form,

it might not represent the actual measure.

So,

Step 3. consider the angles as 3x,3x and2x .

The sum of the angles of the triangle can be expressed using the above relation as,

$\begin{array}{c}3x+3x+2x=180\\ 8x=180\\ x=\frac{180}{8}\\ =22.5\end{array}$

So, each of the angles are given by,

$\begin{array}{c}3x=3\times 22.5\\ =67.5°\end{array}$

$\begin{array}{c}2x=2\times 22.5\\ =45°\end{array}$

Therefore, the angles of the isosceles triangle are,$67.5°$ ,$67.5°$ and$45°$ .