Quadrilaterals and Polygons - Angles Worksheets - Free Printable

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The quadrilateral WUVX has a right angle at W (90°), an angle of 75° at X, and angles at U and V given by expressions: m∠U = 12x + 10 and m∠V = 11x + 1.

The sum of the interior angles of any quadrilateral is 360°. Therefore:

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

Combine like terms:

(90 + 75 + 10 + 1) + (12x + 11x) = 360
176 + 23x = 360

Subtract 176 from both sides:

23x = 184

Divide by 23:

x = 8

Now substitute x = 8 into the expression for m∠V:

m∠V = 11x + 1 = 11(8) + 1 = 88 + 1 = 89°

The correct answer is B) 89°.

Parent Tip: Review the logic above to help your child master the concept of angles in quadrilaterals worksheet.

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Quadrilaterals and Polygons – Angles Worksheets