Question

In a pentagon, two angle are 40° and 60°  and the rest are in the ratio of 5 : 2 : 4. Find the difference between biggest angle and smallest angle of the pentagon.
1. 200° 
2. 160° 
3. 80° 
4. 40° 

Answer 1

Correct Answer - Option 2 : 160° 

Given 

In a pentagon,

Two angle are 40° and 60°

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 side = 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 = 40°  + 60° 

⇒ 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° 

Now,

⇒ Biggest angle = 200° 

⇒ Smallest angle = 40° 

⇒ Difference between biggest angle and smallest angle = 200° - 40° 

⇒ Difference between biggest angle and smallest angle = 160° 

∴  Difference between biggest angle and smallest angle is 160°