Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 1 - Review Exercises - Page 62: 20

Answer

m$\angle$ABC = 98$^{\circ}$

Work Step by Step

Since ray BD bisect $\angle$ABC: m$\angle$ABD = m$\angle$DBC Substitute the values from the problem... 2x + 15 = 3x - 2 Subtract 2x from both sides. 2x - 2x + 15 = 3x - 2x - 2 15 = x - 2 Add 2 to both sides. 15 + 2 = x - 2 + 2 17 = x Substitute the value of x into either of the smaller angles. m$\angle$ABD = 2x + 15 m$\angle$ABD = 2(17) + 15 m$\angle$ABD = 49$^{\circ}$ Since both smaller angles are congruent... m$\angle$ABC = 2(m$\angle$ABD) m$\angle$ABC = 2(49) m$\angle$ABC - 98$^{\circ}$
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