Question

list the angle measures of δrst in order from smallest to largest, given that rt = 48 centimeters, st = 37 centimeters, and rs = 70 centimeters. m∠r < m∠s < m∠t

Explanation:

Step1: Match angles to opposite sides

In a triangle, each angle is opposite a side:

• $m\angle R$ is opposite $ST = 37$ cm
• $m\angle S$ is opposite $RT = 48$ cm
• $m\angle T$ is opposite $RS = 70$ cm

Step2: Order sides by length

Sort the side lengths from smallest to largest:
$37 < 48 < 70$

Step3: Map to corresponding angles

By the triangle angle-side relationship, the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side. So the angles follow the same order as their opposite sides.

Answer:

$m\angle R < m\angle S < m\angle T$