Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 7 - Similarity - Get Ready! - Page 429: 4

Answer

70$^{\circ}$; Angle 4 is a vertical angle of angle 1. Angle 1 is 70$^{\circ}$ and since vertical angles are congruent Angle 4 is 70$^{\circ}$.

Work Step by Step

Angle 4 is a vertical to Angle 1. So, the first step is to find the value of Angle 1. We know that angle 1 is equal to 70$^{\circ}$ since same side interior angles are supplementary - or equal to 180 $^{\circ}$. 180-110=70$^{\circ}$. Angle 4=Angle 1 because of the Vertical Angle Theorem which states that vertical angles are congruent - or equal. Therefore, Angle 4=70$^{\circ}$
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