Question

The angles of a pentagon are in the ratio 3:4:5:7:8. What is the value of the largest angle (in degrees)? 200 160 180 140​

Answer 1

160°

Step-by-step explanation:

Angle sum in pentagon is 540°

3x+4x+5x+7x8x=540°

27x=540°x=20°

largest angle means 8x=8(20°)

=160°

Answer 2

Answer:

160 degrees

Step-by-step explanation:

Sum of all interior angles in a pentagon is equal to 540 degrees.

let the ratios be 3x,4x,5x,7x,8x.

Then,

3x+4x+5x+7x+8x = 540 degrees

14x+5x+8x = 540 degrees

27x = 540 degrees

x = 540/27 degrees

x = 20 degrees

The largest angle is 8x so ,

8x = 20 x 8 degrees

8x = 160 degrees

Therefore, the largest angle is 160 degrees.

Thank you!