Question

1. ∠1 and ∠2 are alternate interior angles formed by a transversal cutting two parallel lines. if ∠1 = 3x + 10 and ∠2 = 5x - 6, what is the value of x?

○ a. 8
○ b. 10
○ c. 18
○ d. 16

Explanation:

Step1: Recall Alternate Interior Angles Theorem

Alternate interior angles formed by a transversal cutting two parallel lines are equal. So, \( \angle 1=\angle 2 \).

Step2: Set Up the Equation

Given \( \angle 1 = 3x + 10 \) and \( \angle 2 = 5x - 6 \), we set them equal: \( 3x + 10 = 5x - 6 \).

Step3: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 10 = 2x - 6 \).
Add 6 to both sides: \( 16 = 2x \).
Divide by 2: \( x = 8 \).

Answer:

a. 8