Question

The interior angles of a pentagon are in the ratio 2 : 4 : 5 : 6 : 7. Find the difference between the largest and the smallest angle.

Answer 1

Answer:

Interior angles of petagon are 80,100,120 and 140.

Hence, Differences of largest and smallest angle is 80...

Answer 2

Step-by-step explanation:

Let the angles of the Pentagon be 4x, 5x, 6x, 7x and 5x.

Let 'n' be the number of sides.

In a regular Pentagon, sum of interior angles = (2n - 4) × 90°

= ( 2 × 5 - 4) × 90°

= 6 × 90°

= 540°

Acc. to the ques.

=> 4x + 5x + 6x + 7x + 5x = 540°

=> 27x = 540°

=> x = 540° / 27

=> x = 20°

The interior angles of the given Pentagon -

1) 4x = 4 × 20° = 80°

2) 5x = 5 × 20° = 100°

3) 6x = 6 × 20° = 120°

4) 7x = 7 × 20° = 140°

5) 5x = 5 × 20° = 100