When a transversal (a line that crosses two parallel lines), it creates eight angles with four special relationships: corresponding angles are equal, alternate interior angles are equal, alternate exterior angles are equal, and co-interior (same-side interior) angles are supplementary.
Imagine a ladder leaning against two horizontal rails (the parallel lines). The ladder is the transversal. At each rail, the ladder makes the same pattern of angles—like a stamp pressed in two places. Corresponding angles are in matching positions at each crossing, and they're always equal when the rails are parallel.
Showing a random 20 of 50 problems.
Example 1
medium
Lines ℓ1 and ℓ2 are crossed by a transversal t. The alternate interior angles are (7x−10)° and (5x+20)°. Are ℓ1 and ℓ2 parallel? If yes, find each angle.
Example 2
medium
A transversal is perpendicular to one of two parallel lines. What angle does it make with the other line?
Example 3
easy
A transversal makes a 55° angle. Its vertical angle is what?
Example 4
medium
Two parallel lines are crossed by two different transversals forming a triangle. The angles where the transversals meet the top line are 50° and 60°. Find the third (apex) angle of the triangle.
Example 5
medium
Why are alternate interior angles equal when the lines are parallel?
Example 6
medium
A transversal cuts parallel lines ℓ1 and ℓ2. An angle in the upper intersection above ℓ1, to the right of the transversal, is 124°. Find the angle in the lower intersection above ℓ2, to the left of the transversal.Find angle x at the lower intersection.
Example 7
medium
Lines AB and CD are parallel, cut by transversal EF. If one angle measures 118°, list the measures of all eight angles.List the measures of all eight angles.
Example 8
challenge
Three parallel lines are cut by a transversal. How many distinct angle measures appear (in general)?
Example 9
medium
Two parallel lines are cut by a transversal. Corresponding angles are (4x+5)° and (2x+35)°. Find x and each angle.Find x and each angle measure.
Example 10
easy
Two parallel lines are cut by a transversal. Two corresponding angles measure (3x)° and (x+50)°. Find x.Corresponding angles are equal. Find x.
Example 11
easy
A transversal crosses parallel lines; one corresponding pair measures 112°. What is its vertical angle?
Example 12
medium
A transversal creates angles where co-interior angles measure (5x+10)° and (3x+30)°. Find x and verify the angles are supplementary.
Example 13
hard
Two parallel lines ℓ1 and ℓ2 are cut by a transversal at points A and B. A point P lies between the lines such that PA and PB form the transversal. If the angles at A and B on the same side are α and β (above ℓ1 at A, below ℓ2 at B, both on the same side), find α+β.
Example 14
easy
A transversal crosses two parallel lines. One of the angles formed is 65°. Find the corresponding angle and the alternate interior angle.Find the corresponding angle and the alternate interior angle.
Example 15
medium
Two parallel lines cut by a transversal: an alternate interior angle is 108°. Find a co-interior (same-side interior) angle.
Example 16
easy
Two parallel lines cut by a transversal: an alternate interior angle is 72°. Find its alternate interior partner.
Example 17
hard
Lines m and n are cut by a transversal. Corresponding angles are (7x−15)° and (4x+27)°. Are lines m and n parallel? If so, find the angle measure.Are lines m and n parallel? Find x and the angle measure.
Example 18
easy
Find the four pairs of angles formed by a transversal cutting parallel lines that have a single name.
Example 19
medium
A transversal crosses two parallel lines. One angle is 3 times its co-interior partner. Find the smaller angle.
Example 20
easy
Two angles formed by a transversal and parallel lines are corresponding. One is 73°. Find the supplement of its corresponding partner.