Geometry: Common Core (15th Edition)

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

Chapter 8 - Right Triangles and Trigonometry - 8-1 The Pythagorean Theorem and It's Converse - Practice and Problem-Solving Exercises - Page 498: 57



Work Step by Step

With isosceles triangles, we need to remember that the base angles are congruent. If the vertex angle is $58^{\circ}$, then we can find the measurement 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 = $180^{\circ} - (58^{\circ})$ Subtract to solve: measure of the base angles = $122^{\circ}$ Since the base angles are congruent, each will be half of $122^{\circ}$. Let's find the measure of just one of the base angles: measure of each base angle = $122^{\circ}/2$ Divide to solve: measure of each base angle = $61^{\circ}$
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