MathematicsIn the given figure, if PT is a tangent of the circle with center O and ∠TPO=25∘, then the measure of x is:

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

Given, PT is a tangent of the circle with center O and ∠TPO=25

°

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

∠ PTO = 90^{o}

.
Hence by the exterior angle formula applied to triangle

OTP

, we get,

x = ∠ PTO + ∠ OPT

\Rightarrow x = 90 + 25

\Rightarrow x = 11 5^{\circ}

So, the measure of x is

11 5^{\circ}

.
Therefore, option 4 is correct.

JEE