Question

value: 3
find the indicated angle measure.
o a. 51°
o b. 78°
o c. 204°
o d. 12°

Explanation:

Step1: Recall angle - sum property of a quadrilateral

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 - radius intersections. The angles between the radii and the tangents are $90^{\circ}$ each, and one of the central angles is $102^{\circ}$. Let the unknown angle be $x$. So, the sum of the angles of the quadrilateral is $90^{\circ}+90^{\circ}+102^{\circ}+x = 360^{\circ}$.

Step2: Solve for $x$

\[

$$\begin{align*} 90 + 90+102+x&=360\\ 282 + x&=360\\ x&=360 - 282\\ x&= 78^{\circ} \end{align*}$$

\]

Answer:

b. $78^{\circ}$