Question

The interior angles of a pentagon are in the ratio 4:5:6:7:5. Find each angle of the Pentagon.
This question is of class 8th chapter quadrilaterals maths book nei star by manoj kesari and anuj jain and please answer this question only if you know the correct answer otherwise it will be reported.​

Answer 1

Answer:

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°

Ans. = The interior angles of the Pentagon are 80° , 100° , 120° , 140° and 100°.

Hope it helps!!!