Question

solve with explanation​

Answer 1

Answer:

largest angle = 280°

Step-by-step explanation:

let the common factor be x

40°+60°+1x+3x+7x=540° ( angle sum property of Pentagon)

100°+ 11x = 540°

11x = 540° - 100°

= 440°

x = 440/11

= 40°

7x=7*40

= 280°

Answer 2

Answer: 280°

Step-by-step explanation:

First we need to find the angle sum property of Pentagon. The formula for that is (n-2)*180 where 'n' means number of sides.

No. Of sides in Pentagon= 5

So, the sum of all the interior angles of pentagon= (5-2)*180

=> 3*180 = 540°

ATQ, angles of the Pentagon are 60°, 40°, 1x, 3x and 7x ( given that, 1:3:7, x represents the common factor in the ratio.

=> 60 + 40 + 1x + 3x + 7x = 540

=> 100 + 11x = 540

=> 11x = 540-100

=> 11x = 440

=> x = 440/11 = 40

The measure of 1x = 1(40) = 40°.

The measure of 3x = 3(40) = 120°.

The measure of 7x = 7(40) = 280°.

40° =40°<60°<120°<280°

Therefore, the largest angle is 280°