Answer: 35
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Explanation:
A full circle is 360 degrees. The pie slices shown represent the various angles of each slice. Each angle expression in that diagram will add up to 360.
Doing this will help us solve for x.
(angleVQR)+(angleRQS)+(angleSQT)+(angleTQU)+(angleUQV) = 360
(21x+4) + (14x-4) + (5x+5) + (5x+5) + (80) = 360
45x+90 = 360
45x = 360-90 ... subtract 90 from both sides
45x = 270
x = 270/45 ..... divide both sides by 45
x = 6
We'll then plug this x value into the angle expression for angle TQU
angle TQU = 5x+5
angle TQU = 5*6+5
angle TQU = 35 degrees
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Extra info:
- angle VQR = 130 degrees
- angle RQS = 80 degrees (same as angle UQV)
- angle SQT = 35 degrees (same as angle TQU)
- Starting at angle VQR, and working clockwise, the five angles are: 130, 80, 35, 35, 80. Note that 130+80+35+35+80 = 360.
