Question

find the indicated angle measure.
66°
o a. 33°
o b. 132°
o c. 114°
o d. 24°

Explanation:

Step1: Recall quadrilateral - angle - sum property

The sum of the interior angles of a quadrilateral is $360^{\circ}$. In the given figure, we have a quadrilateral formed by two radii and two tangent - lines to the circle. The angles between the radii and the tangent - lines are $90^{\circ}$ each. Let the unknown central angle be $x$.

Step2: Set up the angle - sum equation

We know that $90^{\circ}+90^{\circ}+x + 66^{\circ}=360^{\circ}$.

Step3: Solve the equation for $x$

First, simplify the left - hand side: $180^{\circ}+x + 66^{\circ}=360^{\circ}$, then $x+246^{\circ}=360^{\circ}$. Subtract $246^{\circ}$ from both sides: $x = 360^{\circ}-246^{\circ}=114^{\circ}$.

Answer:

C. $114^{\circ}$