Question

question
in △opq, $overline{pq}congoverline{op}$ and m∠p = 121°. find m∠o.
answer attempt 1 out of 2

Explanation:

Step1: Identify isosceles triangle

Since $\overline{PQ}\cong\overline{OP}$, $\triangle OPQ$ is isosceles. So $\angle O\cong\angle Q$.

Step2: Use angle - sum property of triangle

The sum of interior angles of a triangle is $180^{\circ}$. Let $m\angle O = x$ and $m\angle Q=x$ (because base - angles of isosceles triangle are equal), and $m\angle P = 121^{\circ}$. Then $x + x+121^{\circ}=180^{\circ}$.

Step3: Solve the equation

Combine like - terms: $2x+121^{\circ}=180^{\circ}$. Subtract $121^{\circ}$ from both sides: $2x=180^{\circ}- 121^{\circ}=59^{\circ}$. Divide both sides by 2: $x=\frac{59^{\circ}}{2}=29.5^{\circ}$.

Answer:

$29.5^{\circ}$