Five exterior angles of a pentagon are 2x – 20, 2x + 50, 3x + 10, 3x and 50°. A) Find the value of x. B) Which is the largest angle? State the angle measure.

Question

Please answer this as soon as possible. Thank you!

Answer 1

For any polygon, the sum of its exterior angles is 360 degrees.

Add all the measurements together; set them = 360.

So, (2x-20) + (2x + 50) + (3s + 10) + 3x + 50 = 360.

*COMBINE like terms 2x + 2x + 3x + 3x = 10x and -20 + 50 + 10 + 50 = 90.

Now, you have 10x + 90 = 360.

*Solve the two-step equation. 10x + 90 = 360

- 90 - 90

10x = 270

10x/10 = 270/10

x = 27 **Part A

**Part B: Plug in 27 for each X.

Simplify each

2(27) - 20 = 34

2(27) + 50 = 104

3(27) + 10 = 91

3(27) = 81

50

So, 104 is the angle measure of the largest angle.

Hope you were able to follow the step-by-step details to get a better understanding!!

Answer 2

The sum of the exterior angles of a polygon is 360°.

So, 10x + 90 = 360

10x = 270

x = 27