Geometry

Question Analysis

This question is about using the property of congruent angles to find the value of a variable. The main focus is applying the fact that congruent angles have equal measures.

 

Key Concept Explanation

Congruent angles mean that if ∠A ≌ ∠B, then the measure of ∠A is equal to the measure of ∠B, i.e., m∠A = m∠B.

 

Step - by - Step Solution

1. We know that ∠XYZ ≌ ∠HGF. The measure of ∠HGF is 90° (as indicated by the right - angle symbol), and the measure of ∠XYZ is 2x°.

2. Set up the equation based on the congruence property: 2x = 90.

3. Solve the equation for x. Divide both sides of the equation by 2: x = 90÷2 = 45.

 

Common Mistakes

Forgetting that congruent angles have equal measures and not setting up ...