Elementary Geometry for College Students (7th Edition)

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

Chapter 6 - Section 6.1 - Circles and Related Segments and Angles - Exercises - Page 285: 11c


measure of arc $CA=160^{\circ}$

Work Step by Step

The measure of an entire circle is $360^{\circ}$. If you add the three arcs together...$AB+BC+CA$ you have the entire circle. So... arc $AB=2x$, arc $BC=3x$, and arc $AC=4x$. $2x+3x+4x=360$ combine like terms... $9x=360$ Divide both sides by 9... $x=40$ Plug $x=40$ into the $4x$ (the measure of arc $CA$) and the measure of arc $CA=160^{\circ}$.
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