Question

question 20 of 25 if the measure of a tangent-chord angle is 68°, then what is the measure of the intercepted arc inside the angle? a. 68° b. 112° c. 34° d. 136°

Explanation:

Step1: Recall the tangent - chord angle theorem

The measure of a tangent - chord angle is half the measure of its intercepted arc. Let the measure of the intercepted arc be \( x \). The formula is \( \text{Measure of tangent - chord angle}=\frac{1}{2}\times\text{Measure of intercepted arc} \).

Step2: Substitute the given angle into the formula

We know that the measure of the tangent - chord angle is \( 68^\circ \). So we have the equation \( 68^\circ=\frac{1}{2}x \).

Step3: Solve for \( x \)

To solve for \( x \), we multiply both sides of the equation by 2. So \( x = 2\times68^\circ=136^\circ \).

Answer:

D. \( 136^\circ \)