Answers:
- Angle X = 142 degrees
- Angle Y = 142 degrees
Both angles are the same measure
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Explanation:
We have a 5 sided polygon, so this is a pentagon.
For any pentagon, the five interior angles always add to 180(n-2) = 180(5-2) = 540 degrees. The formula 180(n-2) tells us the sum of the interior angles for any polygon with n sides.
The diagram shows the following angle values
- V = 119
- W = 47
- X = m
- Y = m
- Z = 90 (due to the square angle marker)
Both angles X and Y are equal to the same unknown value m. They are both the same measure because they both have the same arc marking.
Adding up those five angles should get us 540 as mentioned earlier
V+W+X+Y+Z = 540
119+47+m+m+90 = 540
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Let's solve for m
119+47+m+m+90 = 540
2m+256 = 540
2m = 540-256
2m = 284
m = 284/2
m = 142
Angle X has the measure of 142 degrees, and so does angle Y.
