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Answer:

x = 8

m∠V = 89°

What We Know

m∠W = 90°

m∠V = 11x + 1

m∠U = 12x + 10

m∠X = 75

The sum of all the angles in a quadrilateral is 360°

Solve For X

m∠W + m∠V + m∠U + m∠X = 360°

Plug what you know into the above equation in the appropriate spots

90 + (11x + 1) + (12x + 10) + 75 = 360

Combine like terms

90 + 11x + 1 + 12x + 10 + 75 = 360

176 + 11x + 12x = 360

176 + 11x + 12x = 360

176 + 23x = 360

23x = 184

Isolate x

x = 8

Find m∠V

Given: m∠V = 11x + 1

Plug in the x you previously found into the equation above and solve

m∠V = 11(8) + 1

m∠V = 88 + 1

m∠V = 89°

User Drew Turner
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