Question

find m∠qpo.

Explanation:

Step1: Identify isosceles triangle

Since $OP = OQ$ (marked by the equal - side symbols), $\triangle OPQ$ is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let $\angle OQP=\angle QPO = x$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. In $\triangle OPQ$, we have $\angle POQ + \angle OQP+\angle QPO=180^{\circ}$. Given $\angle POQ = 41^{\circ}$, so $41^{\circ}+x + x=180^{\circ}$.

Step3: Solve the equation for $x$

Combining like terms, we get $41^{\circ}+2x = 180^{\circ}$. Subtract $41^{\circ}$ from both sides: $2x=180^{\circ}- 41^{\circ}=139^{\circ}$. Then divide both sides by 2: $x=\frac{139^{\circ}}{2}=69.5^{\circ}$.

Answer:

$69.5$