Geometry: Common Core (15th Edition)

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

Chapter 5 - Relationships Within Triangles - 5-6 Inequalities in One Triangle - Lesson Check - Page 328: 2


$\angle C$

Work Step by Step

Let's take a look first at the angles in this triangle. We have an exterior angle, which will be supplementary to the interior angle $\angle A$; therefore, $\angle A$ of the triangle can be calculated by the following equation: $m \angle A = 180 - 85$ Subtract to find the measure of $\angle A$: $m \angle A = 95$ We know that $\angle A$ is the largest angle because the sum of the measures of the other two angles has to be $180^{\circ} - 95^{\circ}$ or $85^{\circ}$. $\overline{BC}$ would be the longest side because it is opposite the largest angle in a triangle where two of the angles are not congruent. This means that the angle opposite the smallest side in this triangle would be the smallest angle; therefore, the angle opposite the shortest side $\overline{AB}$ would be $\angle C$.
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