Geometry

Question Analysis

The main focus is to apply the Hinge Theorem to compare the measures of  and . Given the side lengths of  and , we need to use the theorem to determine the relationship between these two angles.

Key Concept Explanation

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, but the third sides are different, then the larger included angle is opposite the longer third side.

Step - by - Step Solution

1. In  and , we have  and  is common ().

The side  and .

Since  >  (  > ), by the Hinge Theorem, the angle opposite  (which is ) is larger than the angle opposite  (which is

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