Question

the interior angles of a pentagon are in the ratio 2:3:4:5:6 respectively.then the sum of the first and second angle is​

Answer 1

Answer:

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!!!

Answer 2

Explanation:

let the angles be 2x,3x,4x,5x and 6x

we know that,

sum of angles of a Pentagon = 540°

$= > \: 2x + 3x + 4x + 5x + 6x = 540 \\ = > 20x = 540 \\ = > x = 27$

therefore, sum of 1st and second angle= 2x+3x

= 2×27 + 3×27

= 54° + 81°

= 135°ans.