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

Question

asked Jun 20, 2019 10.5k views

2 Answers

Davr · Answer 1 · 2019-06-24T13:57:11+0000

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:-

$m \angle PRS= (1)/(2) m\angle PQR$

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,
$m\angle PQR=2* (m\angle PRS)$

Thus,
$m\angle PQR=2* 68^(0)$

Or
$m\angle PQR=136^(0)$

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