470 CHAPTER 8 Geometry Earlier we learned that quadrilaterals are four-sided polygons, the sum of whose interior angle measures is ° 360 . Quadrilaterals may be classified according to their characteristics, as illustrated in the following summary box. Quadrilaterals Trapezoid Parallelogram Rhombus Two sides are parallel. Both pairs of opposite sides are parallel. Both pairs of opposite sides are equal in length. Both pairs of opposite sides are parallel. The four sides are equal in length. Rectangle Square Both pairs of opposite sides are parallel. Both pairs of opposite sides are equal in length. All the angles are right angles. Both pairs of opposite sides are parallel. The four sides are equal in length. All the angles are right angles. Note that in Example 5 part (b) we could also have determined the measure of angle y as follows. By the definition of a trapezoid, sides AB and CD must be parallel. Therefore, side AD may be considered a transversal and BAD and ADE are alternate interior angles. Recall from Section 8.1 that alternate interior angles have equal measures. Thus, = m BAD m ADE and = m y 130°. Instructor Resources for Section 8.2 in MyLabMath • Objective-Level Videos 8.2 • Animation: Sum of Interior Angles of Polygons • PowerPoint Lecture Slides 8.2 • MyLab Exercises and Assignments 8.2 Example 5 Angles of a Trapezoid Trapezoid ABCD is shown in Fig. 8.24. Now try Exercise 69 1308 D C E B A y x Figure 8.24 a) Determine the measure of the interior angle, x. b) Determine the measure of the exterior angle, y. Solution 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 + + + = ° ° + ° + ° + = ° ° + = ° = ° mDAB mABC mBCD mx m x m x m x 360 130 90 90 360 310 360 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 m x 180° 180° 50° 130°. Thus, the measure of the exterior angle, y, is ° 130 . 7
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