To solve this problem, we need to understand the relationship between a tangent-chord angle and its intercepted arc.
1. Definition and Property:
- A tangent-chord angle is an angle formed by a tangent and a chord that intersect at a point on a circle.
- There is a specific property of tangent-chord angles: the measure of a tangent-chord angle is half the measure of its intercepted arc.
2. Given Information:
- The measure of the tangent-chord angle is [tex]\( 68^\circ \)[/tex].
3. Interpreting the Property:
- According to the property mentioned above, the intercepted arc is twice the measure of the tangent-chord angle.
4. Calculation:
- Measure of the intercepted arc [tex]\( = 2 \times \)[/tex] (measure of the tangent-chord angle)
- Measure of the intercepted arc [tex]\( = 2 \times 68^\circ \)[/tex]
5. Result:
- Measure of the intercepted arc [tex]\( = 136^\circ \)[/tex]
Therefore, the measure of the intercepted arc inside the angle is [tex]\( 136^\circ \)[/tex]. Thus, the correct answer is:
C. [tex]\( 136^\circ \)[/tex].
