Geometry: Common Core (15th Edition)

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

Chapter 7 - Similarity - Common Core Cumulative Standards Review - Selected Response - Page 486: 17


measure of each base angle = $34^{\circ}$

Work Step by Step

With isosceles triangles, we need to remember that the base angles are congruent. If the vertex angle is $112^{\circ}$, then we can find the measure of each of the base angles by using the triangle sum theorem, which states that the sum of the measures of the angles of a triangle equals $180^{\circ}$: measure of the base angles = $180^{\circ} - (112^{\circ})$ Subtract to solve: measure of the base angles = $68^{\circ}$ Since the base angles are congruent, each will be half of $68^{\circ}$. Let's find the measure of just one of the base angles: measure of each base angle = $68^{\circ}/2$ Divide to solve: measure of each base angle = $34^{\circ}$
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