Question 9.2E5: Angles of a Trapezoid Trapezoid ABCD is shown in Fig. 9.24. ......

a)  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°.