Geometry: Common Core (15th Edition)

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

Chapter 8 - Right Triangles and Trigonometry - Common Core Cumulative Standards Review - Selected Response - Page 539: 6



Work Step by Step

The largest angle lies opposite to the longest side. We have the measures of two angles in a triangle, so we need to find the measure of the third angle. We can accomplish this by using the triangle sum theorem, which states that the sum of the measures of the interior angles of a triangle must equal $180^{\circ}$. $m \angle T = 180 - (72 + 55)$ Evaluate what is in parentheses first: $m \angle T = 180 - (127)$ Subtract to solve: $m \angle T = 53^{\circ}$ Now, let's figure out which side lies opposite to which angle: $\angle H$ lies opposite to $\overline{TQ}$. $\angle T$ lies opposite to $\overline{HQ}$. $\angle Q$ lies opposite to $\overline{HT}$. Let's put the angles in order from least to greatest first: $\angle T$ < $\angle Q$ < $\angle H$ Now, we can order the sides by matching them up with the angles that are opposite to them: $\overline{HQ}$ < $\overline{HT}$ < $\overline{TQ}$ The answer is option $H$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.