Question

question
in △pqr, $overline{pq}congoverline{rp}$ and m∠p = 57°. find m∠r.
answer attempt 1 out of 2

Explanation:

Step1: Identify isosceles triangle

Since $\overline{PQ}\cong\overline{RP}$, $\triangle PQR$ is isosceles with base - angles equal. Let $\angle Q=\angle R$.

Step2: Use angle - sum property of triangle

The sum of interior angles of a triangle is $180^{\circ}$. So, $m\angle P + m\angle Q + m\angle R=180^{\circ}$. Substitute $m\angle Q = m\angle R$ and $m\angle P = 57^{\circ}$ into the equation: $57^{\circ}+m\angle R + m\angle R=180^{\circ}$.

Step3: Solve for $m\angle R$

Combine like - terms: $57^{\circ}+2m\angle R=180^{\circ}$. Then $2m\angle R=180^{\circ}- 57^{\circ}=123^{\circ}$. So, $m\angle R=\frac{123^{\circ}}{2}=61.5^{\circ}$.

Answer:

$61.5^{\circ}$