Answer: The interior angles of the Pentagon are 80° , 100° , 120° , 140° and 100°.
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°
I hope it helps