Question

what property justifies setting each expression equal to one another to find the value of x?
options:

• obtuse interior angles are congruent
• alternate interior angles are congruent
• corresponding angles are congruent
• alternate exterior angles are congruent

Explanation:

Step1: Identify angle - type relationship

The two angles $(x + 72)^{\circ}$ and $(2x+12)^{\circ}$ are alternate interior angles. When two parallel lines are cut by a transversal, alternate interior angles are congruent. So we set up the equation $x + 72=2x + 12$.

Step2: Solve the equation for x

Subtract x from both sides: $72=2x - x+12$, which simplifies to $72=x + 12$. Then subtract 12 from both sides: $x=72 - 12=60$.

Answer:

$x = 60$