Let C be a circle with centre O and PQ be a minor arc on C. Let R and S be two points on the major arc of PQ on C. If PQ subtends an angle 80° at O, find ∠PRQ and ∠PSQ, respectively.

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Accepted Answer

Given that PQ is a minor arc of the circle with center O, and it subtends an angle of 80° at O. R and S are two points on the major arc of PQ.

According to the circle theorem, the angle subtended by an arc at the center (O) is twice the angle it subtends at any point on the remaining circumference (on the same segment).

So, the angle subtended by PQ at any point (R or S) on the major arc is:
$$
\angle PRQ = \angle PSQ = \frac{1}{2} 	imes 80^\circ = 40^\circ
$$

Therefore, both ∠PRQ and ∠PSQ are 40°.

So, the correct answer is option 4: 40° and 40°.

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