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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