Question

If the measure of a tangent-chord angle is 68 degrees, then what is the measure of the intercept arc inside the angle

A.112

B.68

C.34

D.136

Answer 1

Please find the attached diagram for a better understanding of the question.

For solving this question we will make use of a theorem which says: Tangent-chord angles are equal to half the measure of the intercepted arc.

Thus, if we use this theorem in our diagram, we will arrive at this equation:-

$m \angle PRS= \frac{1}{2} m\angle PQR$

Now, we are given that $m\angle PRS=68^{0}$ (please note that $\angle PRS$ is the angle between the tangent and the chord.)

Therefore, $m\angle PQR=2\times (m\angle PRS)$

Thus, $m\angle PQR=2\times 68^{0}$

Or $m\angle PQR=136^{0}$

Therefore, we conclude that Option D is the correct answer.

Answer 2

The answer to this is D!

Hope I helped