When a line crosses two parallel lines, the angles it makes come in pairs. Corresponding, alternate interior and alternate exterior pairs are equal. Co-interior pairs, the ones on the same side of the transversal and between the parallels, add to 180. Everything on the page is one of those two facts.
Two parallel lines are cut by a transversal. One angle measures 65∘. Find its co-interior angle
Co-interior angles add to 180.
180 minus 65.
The answer is 115∘.
Where students go wrong
Assuming every pair is equal. Four of the five pairs are, and co-interior is the one that adds to 180 instead. If your two angles are on the same side of the transversal and between the parallel lines, they are supplementary, not equal.
Also called transversal angles, corresponding angles, alternate interior angles or co-interior angles.
What you can put on this worksheet
With a diagram, angles numbered 1 to 8
In the figure, m∠5=150∘. Find m∠6→ 30∘
Without a diagram, described in words
Two parallel lines are cut by a transversal. One angle measures 55∘. Find its alternate exterior angle→ 55∘
Without a diagram, solve for x
Two parallel lines are cut by a transversal. A pair of alternate exterior angles measure 2x+104 and 3x+96. Find x→ 8
Questions about these worksheets
Yes. Every parallel lines and transversals sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the parallel lines and transversals questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 3: with a diagram, angles numbered 1 to 8, without a diagram, described in words and without a diagram, solve for x. Tick as many as you want and set how many of each, or let it spread them evenly.
Assuming every pair is equal. Four of the five pairs are, and co-interior is the one that adds to 180 instead. If your two angles are on the same side of the transversal and between the parallel lines, they are supplementary, not equal.