Question

find the measure of ∠nqo. write your answer as a whole number or a decimal. m∠nqo =

Explanation:

Step1: Recall circle - angle relationship

The sum of the central - angle measures of a circle is 360°. Let the measure of the arc $MN$ be $x$. Then $x + 62^{\circ}+94^{\circ}=360^{\circ}$.

Step2: Solve for arc $MN$

$x=360^{\circ}-(62^{\circ} + 94^{\circ})=360^{\circ}-156^{\circ}=204^{\circ}$.

Step3: Use the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. $\angle NQO$ is an inscribed angle that intercepts arc $NO$. The measure of arc $NO = 62^{\circ}$.

Step4: Calculate $\angle NQO$

By the inscribed - angle theorem, $m\angle NQO=\frac{1}{2}\text{ measure of arc }NO$. So $m\angle NQO=\frac{62^{\circ}}{2}=31^{\circ}$.

Answer:

$31$