Answer: D) 12
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Work Shown:
The smaller angles UVN and NVW add up to the largest angle UVW.
This is due to the angle addition postulate.
(angle UVN) + (angle NVW) = angle UVW
(6x+13) + (46) = 11+10x
6x + 59 = 11 + 10x
6x - 10x = 11 - 59
-4x = -48
x = -48/(-4)
x = 12
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Extra info:
If you're curious about the angles, then we use that x value to find them
- angle UVN = 6x+13 = 6*12+13 = 72+13 = 85 degrees
- angle NVW = 46 degrees
- angle UVW = 11+10x = 11+10*12 = 11 + 120 = 131 degrees
Note how 85+46 = 131 to show that (angle UVN) + (angle NVW) = angle UVW is a true equation. This confirms our answer for x.
