Question

Find the value of the variable. Then find the angle measures of the polygon.

The numbers are 2x° 2(x-1) (5x+2°)
Please help!!! 40 points and I need to show my work!!!!

Answer 1

first set up the equation (sum of the angles is 180)

2x + 2(x-1) + (5x +2) = 180

distribute:
2x + 2x -2 + 5x +2 = 180

combine like terms:
9x = 180
solve for x:

x = 20

SO:

2x° = 2(20) = 40 degrees
2(x-1)° = 2(20) - 2 = 40 - 2 = 38 degrees
5x + 2°= 5(20) + 2 = 100 + 2=102 degrees

check: 40 + 38 + 102 = 180