Inscribed angle from a given central angle: O is the centre of the circle and ∠QOR = 50°. Find the measure (in degrees) of ∠RPQ.

Introduction / Context:Inscribed angles that subtend the same arc as a given central angle measure exactly half the central angle. This is a fundamental property of circles.

Given Data / Assumptions:

• Central angle ∠QOR = 50° subtends arc QR.
• Point P lies on the circle, so ∠RPQ is an inscribed angle intercepting the same arc QR.

Concept / Approach:Inscribed angle theorem: inscribed angle = (1/2) × corresponding central angle for the same arc.

Step-by-Step Solution:

Verification / Alternative check:All inscribed angles standing on arc QR are equal; each is half of the 50° central angle.

Why Other Options Are Wrong:20°, 30°, 15°, 35° are not half of 50°.

Common Pitfalls:Confusing inscribed angle with central angle or doubling instead of halving.

Final Answer:25