Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 2 - Section 2.4 - The Angles of a Triangle - Exercises - Page 99: 50

Answer

135 degrees.

Work Step by Step

Angle A and angle B add to 90 degrees, for they are in the same triangle as the right angle. They are each bisected, forming triangle AEB. Because they add up to 90 degrees, the sum of each of them halved (because they are bisected) is 45 degrees. This means that angle AEB is 135 degrees. This angle is a vertical angle to angle FED, so angle FED equals 135 degrees.
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