Question

In the given figure, if PT is a tangent of the circle with center O and $\angle TPO={25}^{\circ }$, then the
the measure of x is :

• A. ${120}^{\circ }$
• B. ${125}^{\circ }$
• C. ${110}^{\circ }$
• D. ${115}^{\circ }$

Answer 1

The correct option is D ${115}^{\circ }$

Since tangent is perpendicular to radius at the point of contact, we have:

$\angle PTO={90}^o$.

Hence by the exterior angle formula applied to triangle $OTP$, we get:

$x=90+25={115}^o$.

So option D is the correct answer.