Question

quadrilateral mnpq is inscribed in circle o. segment mn is part of ray mr. if (mangle pnr = 95^{circ}), which of the following angles must have a measure of (95^{circ})?
a (angle m)
b (angle q)
c (angle n)
d (angle p)

Explanation:

Step1: Recall property of cyclic quadrilateral

In a cyclic quadrilateral, an exterior - angle is equal to the interior - opposite angle.

Step2: Identify exterior and interior - opposite angles

$\angle PNR$ is an exterior angle of cyclic quadrilateral $MNPQ$. The interior - opposite angle to $\angle PNR$ is $\angle Q$. So, $m\angle Q=m\angle PNR$.

Answer:

B. $\angle Q$