Question

question in △opq, $overline{pq}congoverline{op}$ and m∠o = 56°. find m∠q.

Explanation:

Step1: Identify the triangle type

Since $\overline{PQ}\cong\overline{OP}$, $\triangle OPQ$ is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let $\angle Q=\angle O$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. In $\triangle OPQ$, we know that $\angle O = 56^{\circ}$, and let $\angle Q=x$ and $\angle P=x$ (because of the isosceles - triangle property). So, $\angle O+\angle P+\angle Q = 180^{\circ}$, which gives $56^{\circ}+x + x=180^{\circ}$.

Step3: Solve the equation for $x$

Combine like terms: $56^{\circ}+2x = 180^{\circ}$. Subtract $56^{\circ}$ from both sides: $2x=180^{\circ}- 56^{\circ}=124^{\circ}$. Divide both sides by 2: $x=\frac{124^{\circ}}{2}=62^{\circ}$.

Answer:

$62^{\circ}$