Question

value: 3
find x.
a. 136
b. 18
c. 64
d. 19

Explanation:

Step1: Recall quadrilateral - circle property

The sum of the interior angles of a quadrilateral formed by two radii and two tangents to a circle is 360°. The two angles where the radii meet the tangents are 90° each.

Step2: Set up an equation

Let the angle at the center be $\theta=(2x + 8)^{\circ}$ and the non - right angle of the quadrilateral be 44°. Then, $90^{\circ}+90^{\circ}+(2x + 8)^{\circ}+44^{\circ}=360^{\circ}$.

Step3: Simplify the left - hand side

$224^{\circ}+2x=360^{\circ}$.

Step4: Solve for x

Subtract 224° from both sides: $2x=360^{\circ}-224^{\circ}=136^{\circ}$. Then divide both sides by 2: $x = 68^{\circ}\div2=64^{\circ}$.

Answer:

C. 64