Question

in △pqr, $overline{pq}congoverline{rp}$ and m∠p = 57°. find m∠r.

Explanation:

Step1: Identify the triangle type

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

Step2: Use angle - sum property of a triangle

The sum of angles in a triangle is $180^{\circ}$. Let $m\angle R = m\angle Q=x$. Then $m\angle P + m\angle Q+m\angle R=180^{\circ}$. Substituting the values, we get $57^{\circ}+x + x=180^{\circ}$.

Step3: Solve the equation

Combining like - terms, $57^{\circ}+2x = 180^{\circ}$. Subtract $57^{\circ}$ from both sides: $2x=180^{\circ}- 57^{\circ}=123^{\circ}$. Then divide both sides by 2: $x=\frac{123^{\circ}}{2}=61.5^{\circ}$.

Answer:

$61.5^{\circ}$