Two angles of a pentagon are in the ratio 2:3. The others are 60o each. Calculate the smaller of the two angles

Analyze the question: The sum of the interior angles of a pentagon is (n − 2) × 180° = 3 × 180° = 540°. (This is actually a Mathematics question, not Physics.)

Step-by-step solution:

A pentagon has 5 angles. Three of them are 60° each, so they total 180°.

The remaining two angles = 540° − 180° = 360°.

They are in the ratio 2:3, so the total number of parts is 5.

• One part = 360° ÷ 5 = 72°
• Smaller angle = 2 × 72° = 144°
• Larger angle = 3 × 72° = 216°

Check: 144° + 216° + 3(60°) = 360° + 180° = 540° ✓

(Note that the larger angle is 216°, a reflex angle, so the pentagon is concave. That is fine for this question.)

Tip: For any polygon, use the sum of interior angles = (n − 2) × 180°. Subtract the known angles first, then share the remainder in the given ratio.