Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 2 - Section 2.4 - An Introduction to Problem Solving - Exercise Set: 20

Answer

The measure of each angle is 65°, 65°, 115°, and 115°.

Work Step by Step

Opposite angles of a parallelogram have the same measure and the sum of the four angles is 360°. Let the non-equal angles be x and y. Hence, $2x+2y=360$ $2(x+y)=360$ $x+y=180$ The problem tells us that one angle of the parallelogram is 15° less than twice the measure of the angle next to it: $x=2y-15$ Substitute into $x+y=180$ $2y-15+y=180$ $3y=195$ $y=65°$ $x+65=180$ $x=115°$ So, the measure of each angle is 65°, 65°, 115°, and 115°. Check: $65+65+115+115=360$ And $2*65-15=115$
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