In a pentagon, two angles are 50° and 50° and the rest are in the

1.	In a pentagon, two angles are 50° and 50° and the rest are in the ratio of 15 : 2 : 5. Find the smallest angle of the pentagon.1. 50° 2. 30°3. 40°4. 25°
Answer» Correct Answer - Option 3 : 40° Given Two angle are 50° and 50° The rest are in the ratio = 15 : 2 : 5 Concept Sum of all interior angles of a regular polygon = (n - 2) × 180° Calculation Number of side = 5 ⇒ Sum of all interior angles of a pentagon = (5 - 2) × 180° = 3 × 180° = 540° Now, Two angles = 50° + 50° = 100° Sum of rest of the angles = 540° - 100° = 440° Let the ratio of sides in x ⇒ 15x + 2x + 5x = 440° ⇒ 22x = 440° ⇒ x = 20° Now, 15 × 20° = 300° 2 × 20° = 40° 4 × 20° = 80° ∴ Smallest angle is 40°

In a pentagon, two angles are 50° and 50° and the rest are in the ratio of 15 : 2 : 5. Find the smallest angle of the pentagon.1. 50° 2. 30°3. 40°4. 25°

Answer» Correct Answer - Option 3 : 40°

Given

Two angle are 50° and 50°

The rest are in the ratio = 15 : 2 : 5

Concept

Sum of all interior angles of a regular polygon = (n - 2) × 180°

Calculation

Number of side = 5

⇒ Sum of all interior angles of a pentagon = (5 - 2) × 180° = 3 × 180° = 540°

Now,

Two angles = 50° + 50° = 100°

Sum of rest of the angles = 540° - 100° = 440°

Let the ratio of sides in x

⇒ 15x + 2x + 5x = 440°

⇒ 22x = 440°

⇒ x = 20°

Now,

15 × 20° = 300°

2 × 20° = 40°

4 × 20° = 80°

∴ Smallest angle is 40°