Question

what is the relationship between corresponding angles when a transversal intersects two parallel lines?
a. they are supplementary.
b. they are complementary
c. they add up to 90 degrees
d. they are equal

a transversal intersects two parallel lines. one alternate exterior angle is 3x - 20 degrees and its pair is 2x + 10 degrees. find x.
a. 30
b. 40
c. 20
d. 50

Explanation:

Step1: Recall angle - relationship property

When a transversal intersects two parallel lines, corresponding angles are equal.

Step2: Recall alternate - exterior - angle property

When a transversal intersects two parallel lines, alternate exterior angles are equal. So we set up the equation $3x - 20=2x + 10$.

Step3: Solve the equation for $x$

Subtract $2x$ from both sides: $3x-2x-20=2x - 2x+10$, which simplifies to $x-20 = 10$. Then add 20 to both sides: $x=10 + 20$, so $x = 30$.

Answer:

1. d. They are equal
2. a. 30