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.
