Geometry

Question Analysis

The main focus is applying the Hinge Theorem to compare the lengths of  and . Given the angles in  and , along with the common side , we use the theorem to determine the relationship between these two sides.

Key Concept Explanation

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

Step - by - Step Solution

1. In  and ,  is common.

The included angle  ∠YXM = 43° and ∠ZXM = 42°.

Since ∠YXM > ∠ZXM  (  > ), by the Hinge Theorem, the side opposite ∠YXM (which is

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