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

1.	In a pentagon, two angles are 50° and 50° and the rest are in the ratio of 5 : 2 : 4. Find the biggest angle of the pentagon.1. 440° 2. 200° 3. 160° 4. 80°
Answer» Correct Answer - Option 2 : 200° Given In a pentagon, Two angle are 50° and 50° The rest are in the ratio = 5 : 2 : 4 Concept Sum of all interior angles of a regular polygon = (n - 2) × 180° Calculation Number of sides = 5 ⇒ Sum of all interior angles of a pentagon = (5 - 2) × 180° ⇒ Sum of all interior angles of a pentagon = 3 × 180° ⇒ Sum of all interior angles of a pentagon = 540° Now, ⇒ Two angles = 50° + 50° ⇒ Two angles = 100° ⇒ Sum of rest of the angles = 540° - 100° ⇒ Sum of rest of the angles = 440° Let the ratio of sides in x ⇒ 5x : 2x : 4x ⇒ 5x + 2x + 4x = 440° ⇒ 11x = 440° ⇒ x = (440°/11) ⇒ x = 40° Now, ⇒ 5 × 40° = 200° ⇒ 2 × 40° = 80° ⇒ 4 × 40° = 160° ∴ Biggest angle is 200°

In a pentagon, two angles are 50° and 50° and the rest are in the ratio of 5 : 2 : 4. Find the biggest angle of the pentagon.1. 440° 2. 200° 3. 160° 4. 80°

Answer» Correct Answer - Option 2 : 200°

Given

In a pentagon,

Two angle are 50° and 50°

The rest are in the ratio = 5 : 2 : 4

Concept

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

Calculation

Number of sides = 5

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

⇒ Sum of all interior angles of a pentagon = 3 × 180°

⇒ Sum of all interior angles of a pentagon = 540°

Now,

⇒ Two angles = 50° + 50°

⇒ Two angles = 100°

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

⇒ Sum of rest of the angles = 440°

Let the ratio of sides in x

⇒ 5x : 2x : 4x

⇒ 5x + 2x + 4x = 440°

⇒ 11x = 440°

⇒ x = (440°/11)

⇒ x = 40°

Now,

⇒ 5 × 40° = 200°

⇒ 2 × 40° = 80°

⇒ 4 × 40° = 160°

∴ Biggest angle is 200°