Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 6 - Section 6.1 - Circles and Related Segments and Angles - Exercises: 13d

Answer

$m\angle ABC=72^{\circ}$

Work Step by Step

We are given that chords $AB$ and $AC$ are congruent. Therefore, $\triangle ABC$ is an isosceles triangle. Also, we found that the $m\angle A=36^{\circ}$. Subtract the vertex angle from $180$ and divide the resulting number by two (the two base angles) and we will find the $m\angle ABC$. $180-36=144\div2=72$ $m\angle ABC=72^{\circ}$
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