Question

if the measure of a tangent - chord angle is 68°, then what is the measure of the intercepted arc inside the angle?
a. 112°
b. 68°
c. 136°
d. 34°

Explanation:

Step1: Recall the tangent - chord angle formula

The measure of a tangent - chord angle is half the measure of the intercepted arc. Let the measure of the tangent - chord angle be $\theta$ and the measure of the intercepted arc be $m$. Then $\theta=\frac{1}{2}m$.

Step2: Solve for the intercepted arc

Given $\theta = 68^{\circ}$, we can solve for $m$ by multiplying both sides of the equation $\theta=\frac{1}{2}m$ by 2. So $m = 2\theta$. Substituting $\theta = 68^{\circ}$, we get $m=2\times68^{\circ}=136^{\circ}$.

Answer:

C. $136^{\circ}$