State true or false.PQ is a tangent drawn from a point P to a circle with center

Question

State true or false.
PQ is a tangent drawn from a point P to a circle with center O and QOR is a diameter of the circle such that ∠POR =

120^{\circ}

, then ∠OPQ is

30^{\circ}

Options:

A . True

B . False

Answer: Option A
:
A

Given that

∠ P O R = 120^{\circ}

We know that

∠

OQP is

90^{\circ}

Through external angle theorem

∠ P O R = ∠ O Q P + ∠ O P Q

\Rightarrow 120^{\circ} = 90^{\circ} + ∠ O P Q

∠ O P Q = 120^{\circ} - 90^{\circ}

∠ O P Q = 30^{\circ}

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