Sector angle from area and radius: The area of a circular sector is 462 sq cm and the circle’s radius is 21 cm. Find the sector’s central angle (in degrees).

Introduction / Context:Sector area relates to the full circle area by the angle fraction θ/360. With tidy numbers, the computation becomes clean using π = 22/7.

Given Data / Assumptions:

• Sector area A_sector = 462 cm^2.
• Radius r = 21 cm ⇒ full circle area A_circle = πr^2.

Concept / Approach:A_sector = (θ/360) * πr^2 ⇒ θ = 360 * A_sector / (πr^2).

Step-by-Step Solution:

Verification / Alternative check:Plug back: (120/360)*1386 = 462, consistent.

Why Other Options Are Wrong:90°, 60°, 30°, 150° do not satisfy the exact proportion with area 462.

Common Pitfalls:Forgetting to divide by 360 or using diameter instead of radius in the area.

Final Answer:120°