Geometry: Common Core (15th Edition)

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

Chapter 4 - Congruent Triangles - Chapter Test - Page 277: 9

Answer

$x = 36$

Work Step by Step

1. Two angles in one triangle are marked congruent to two angles in the other triangle. 2. An included line from one triangle is marked congruent to an included line from the other triangle. Now, we have two angles and an included side on one triangle congruent to two angles and an included side on another triangle; therefore, we can use the ASA postulate to prove that the two triangles are congruent. So if two triangles are congruent, then their angles and sides are congruent. If two angles are congruent to each other, then we can set these angles equal to each other to find the value of $x$: $3x = 108$ Divide each side by $3$ to solve for $x$: $x = 36$
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