Question 8.2.5: Angles of a Trapezoid Trapezoid ABCD is shown in Fig. 8.24. ......

A Survey of Mathematics with Applications [1175400]

Angles of a Trapezoid Trapezoid

ABCD is shown in Fig. 8.24.

a) Determine the measure of the interior angle, x.

b) Determine the measure of the exterior angle, y.

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a) Because of the right angle symbols, we know that each of the two right angles in trapezoid ABCD has a measure of 90°. We also know that the sum of the interior angles in any quadrilateral is 360°. Therefore, we have

m∡DAB + m∡ABC + m∡BCD + m∡x = 360°

130° + 90° + 90° + m∡x = 360°

310° + m∡x = 360°

m∡x = 50°

Thus, the measure of the interior angle, x, is 50°.

b) Angle x and angle y are supplementary angles. Therefore, m∡x + m∡y = 180° and m∡y = 180° – m∡x = 180° – 50° = 130°. Thus, the measure of the exterior angle, y, is 130°.

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