Question

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

Answer 1

Answer:

The value of x is 43, the angle measures of the polygon are as follows:

top left = 129

top right = 86

bottom left = 55

bottom right = 90

Step-by-step explanation:

I calculated x with the following equation.

3x + 2x + (x + 12) + (2x + 4) = 360

Since all of the angles of this polygon add up to 360, I just put the angle measures on one side and 360 on the other. This is essentially like saying 360 = 360. Now all that is left to do is simplify and calculate the value of x.

5x + (x + 12) + (2x + 4) = 360

8x + 16 = 360

8x = 344

x = 43

Next, I plug the angle's into their expressions to solve for their individual values.

top left:

3x

3(43)

129

top right:

2x

2(43)

86

bottom left:

(x + 12)

(43 + 12)

55

bottom right:

(2x + 4)

[2(43) + 4]

(86 + 4)

90

All that is left to do is check our answer by adding up all the angles to see if they equal 360.

129 + 86 + 55 + 90

360

Because this equals 360, this answer is correct.