Geometry

Question Analysis:
This question combines CPCTC with solving an algebraic equation for an angle measure.
The main focus is on using the fact that corresponding angles of congruent triangles are equal to set up and solve an equation.

Key Concept Explanation:
Since △GHI ≅ △JKL, ∠H corresponds to ∠K.
So, we can set up an equation based on the equality of their angle measures.

Step - by - Step Solution:
Given △GHI ≅ △JKL, so ∠H = ∠K.
Substitute the given expressions for ∠H and ∠K:
We have the equation 5x - 10 = 3x + 20.
Solve the equation for x:
Subtract 3x from both sides: 5x - 3x - 10 = 3x - 3x + 20.
This simplifies to 2x - 10 = 20.
Add 10 to both sides: 2x - 10 + 10 = 20 + 10.
So, 2x = 30.
Divide both sides by 2: 2x/2 = 30/2, which gives x = 15.

Common Mistakes:
Setting up the equation incorrectly, for example, writing 5x - 10+3x + 20 = 0 instead of 5x - 10 = 3x + 20.
Making errors ...