Question

find the unknown angle measures. m∠b =

m∠c =

Explanation:

Step1: Identify isosceles triangle

The triangle has two equal - side markings, so $\angle B=\angle A$.
Since $\angle A = 61^{\circ}$, then $\angle B=61^{\circ}$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle C$ be the unknown angle. So, $\angle A+\angle B+\angle C = 180^{\circ}$.
Substitute $\angle A = 61^{\circ}$ and $\angle B = 61^{\circ}$ into the equation: $61^{\circ}+61^{\circ}+\angle C=180^{\circ}$.
Then $\angle C=180^{\circ}-(61^{\circ} + 61^{\circ})=180^{\circ}-122^{\circ}=58^{\circ}$.

Answer:

$m\angle B = 61^{\circ}$
$m\angle C = 58^{\circ}$