Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 4 - Section 4.2 - The Parallelogram and Kite - Exercises - Page 186: 36

Answer

a) $115^{\circ}$ b) $65^{\circ}$

Work Step by Step

a) Since the two lines that intersect to form the angle are bisectors, 2 angles can be determined in the triangle. The angle formed by the bisectors can be calculated by taking the total sum of internal angles of a triangle and subtracting the bisected angles. $180^{\circ}-20^{\circ}-45^{\circ}=115^{\circ}$ b) Since RT is a straight line, the angle formed between the other 2 bisectors can be determined by subtracting the angle obtained in part a from $180^{\circ}$, which is the angle of a straight line. $180^{\circ}-115^{\circ}=65^{\circ}$
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