Question

1. two alternate interior angles measure $x$ and $3x - 30$. solve for $x$ if the lines are parallel.

a. 14
b. 15
c. 17
d. 16

Explanation:

Step1: Recall angle - property

When two lines are parallel, alternate - interior angles are equal. So we set up the equation $x = 3x-30$.

Step2: Rearrange the equation

Subtract $x$ from both sides: $0=3x - x-30$, which simplifies to $0 = 2x-30$.

Step3: Solve for $x$

Add 30 to both sides: $30 = 2x$. Then divide both sides by 2: $x=\frac{30}{2}=15$.

Answer:

B. 15