Question

if one corresponding angle measures 110 degrees, what is the measure of the other corresponding angle?
a. 110 degrees
b. 90 degrees
c. 70 degrees
d. 120 degrees
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. 25
b. 30
c. 50
d. 40

Explanation:

Step1: Recall corresponding - angles property

When two parallel lines are cut by a transversal, corresponding angles are congruent.

Step2: Determine the measure of the other corresponding angle

Since one corresponding angle measures 110 degrees, the other corresponding angle also measures 110 degrees.

Step3: Recall alternate - interior angles property

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. So, we set the two given alternate - interior angles equal to each other: \(2x + 15=3x - 25\).

Step4: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(15=x - 25\). Then add 25 to both sides: \(x=15 + 25=40\).

Answer:

a. 110 degrees
d. 40