Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 6 - Polygons and Quadrilaterals - Chapter Review - Page 423: 34


$m \angle 1 = 80^{\circ}$ $m \angle 2 = 100^{\circ}$ $m \angle 3 = 100^{\circ}$

Work Step by Step

According to theorem 6-19, the base angles of an isosceles trapezoid are congruent; therefore, if one of the base angles is $80^{\circ}$, the other base angle, $\angle 1$, is $80^{\circ}$. The other two angles of this trapezoid are supplementary to these base angles and are congruent to one another. Let's set the angles equal to $80^{\circ}$ subtracted from $180^{\circ}$: $m \angle 2 = m \angle 3 = 180^{\circ} - 80^{\circ}$ Subtract to solve: $m \angle 2 = m \angle 3 = 100^{\circ}$
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