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 7 - Section 7.2 - Concurrence of Lines - Exercises - Page 336: 40

Answer

49 degrees

Work Step by Step

We call the measure of C equal to x. We call the measure of CEB y. We call the measure of angle EBG z. Since the sum of angles is always 180 degrees for a triangle, we find: $$ .5x+121+z=180 \\ .5x+y+59=180 \\ 2z+y-108+x=180$$ Solving, we find that the measure of angle C is $\frac{98}{2} = 49^{\circ}$
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