Question

1. if one angle of a pair of alternate interior angles is $2x + 15$ and the other is $3x - 25$, find $x$ when the lines are parallel.

a. 50
b. 30
c. 40
d. 25

Explanation:

Step1: Recall property of alternate - interior angles

When two lines are parallel, alternate - interior angles are equal. So, we set up the equation $2x + 15=3x - 25$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides: $2x+15 - 2x=3x - 25-2x$, which simplifies to $15=x - 25$.

Step3: Isolate $x$

Add 25 to both sides: $15 + 25=x-25 + 25$. So, $x = 40$.

Answer:

C. 40