Geometry

Question Analysis

The key is to use the Angle - Side Relationship Theorem. First, we need to find the measure of the third angle in . Then, based on the theorem which states that the longest side is opposite the largest angle and the shortest side is opposite the smallest angle, we can order the sides.

Key Concept Explanation

The Angle - Side Relationship Theorem: In a triangle, the side opposite the largest angle is the longest, and the side opposite the smallest angle is the shortest. This is a fundamental property in triangle geometry that helps in relating the lengths of sides to the measures of their opposite angles.

Step - by - Step Solution

1. Find the measure of :

Since the sum of the interior angles of a triangle is , and we know  and .

Then .

2. Order the angles from largest to smallest:

We have ,

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