Given:
Line NO is tangent to the circle at P.
To determine the mWe also note the rule that when the vertex of the angle is on a circle, the measure of angle is half the measure of its intercepted arc. So,
[tex]m\angle NPQ=\frac{93}{2}=46.5\degree[/tex]
Since NO is a straight line, the angle is 180°. Hence, we can get the m[tex]\begin{gathered} m\angle NPQ+m\angle OPQ=180 \\ 46.5+m\angle OPQ=180 \\ Simplify\text{ and rearrange} \\ m\angle OPQ=180-46.5 \\ m\angle OPQ=133.5\degree \end{gathered}[/tex]Therefore, the answer is:
[tex]m\operatorname{\angle}OPQ=133.5\operatorname{\degree}[/tex]
