If the measure of a tangent chord angle is 68 degrees then what is the measure of the intercepted arc inside the angle

136°

Explanation:

Theorem: The measure of the angle formed by a tangent and a chord is equal to one-half the measure of the intercepted arc.

In the diagram below, PR is the chord, PRS is the tangent, and PQR is the intercepted arc.

Per the theorem,

mPRS = ½mPQR

mPQR = 2mPRS = 2 × 68° = 136°

The measure of the intersected arc is 136°.

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