Correct Answer - Option 2 : 92°
Given
The angles of a pentagon are x°, (x - 10)°, (x + 20)°, (2x - 44)°, and (2x - 70)°
Concept
Sum of all interior angles of a regular polygon = (n - 2) × 180°
Calculation
⇒ n = 5
⇒ Sum of all interior angles of a regular polygon = (5 - 2) × 180°
⇒ Sum of all interior angles of a regular polygon = 3 × 180°
⇒ Sum of all interior angles of a regular polygon = 540°
Now,
⇒ x + (x - 10)° + (x + 20)° + (2x - 44)° + (2x - 70)° = 540
⇒ x + x - 10° + x + 20° + 2x - 44° + 2x - 70° = 540°
⇒ (x + x + x + 2x + 2x) + (20° - 10° - 44° - 70°) = 540°
⇒ 7x - 104° = 540°
⇒ 7x = 540° + 104°
⇒ 7x = 644°
⇒ x = (644°/7)
⇒ x = 92°
∴ x is 92°
