Question

given two lines l and m cut by a transversal t, and ∠1 and ∠2 are alternate interior angles. if ∠1 = 3x + 10 and ∠2 = 5x - 14, and l || m, find x.

Explanation:

Step1: Recall angle - property

When two parallel lines are cut by a transversal, alternate - interior angles are equal. So, $\angle1=\angle2$.

Step2: Set up the equation

Set $3x + 10=5x−14$.

Step3: Solve for x

First, move the x - terms to one side: $10 + 14=5x−3x$.
$24 = 2x$.
Then, divide both sides by 2: $x=\frac{24}{2}=12$.

Answer:

$x = 12$