Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 4 - Section 4.4 - The Trapezoid - Exercises - Page 213: 45

Answer

150 and 144

Work Step by Step

Since it is a trapezoid, corresponding angles are supplementary. Since we do not know which angles are corresponding, we must consider B being corresponding with each of the given angles: $\frac{x}{2} + 10 + \frac{x}{3} + 50 = 180 \\ \frac{5x}{6} = 120 \\ x = 144$ OR $\frac{x}{3} + 50 + \frac{x}{5} + 50 = 180 \\ \frac{8x}{15} = 80 \\ x = 150$
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