Angles with parallel lines

Mathematics · Geometry · ages 12-14

Name ______________________ Date ____________

A Z-shape is formed between two angles on parallel lines cut by a transversal. What type of angle pair is this?
- Co-interior angles
- Alternate angles
- Corresponding angles
Two parallel lines are cut by a transversal. Which of these equal-angle pairs could be a co-interior pair?
- Two 70 degree angles
- Two 90 degree angles
- Two 110 degree angles
Two parallel lines are cut by a transversal. Two interior openings sit between the lines on the same side of the transversal. One measures 64 degrees. What do the two co-interior angles add up to, in degrees?
Answer: ______________
Two parallel lines are crossed by a transversal, forming an F-shape between two angles. What are these angles called?
- Corresponding angles
- Alternate angles
- Co-interior angles
Two parallel lines are cut by a transversal. A co-interior pair is marked (4x) degrees and (2x) degrees. Which equation is correct?
- 4x = 2x
- 4x - 2x = 180
- 4x + 2x = 180
Why are alternate interior angles equal when a transversal crosses two parallel lines?
- They are always half of the co-interior angle
- They match only when the transversal is perpendicular
- Translation matches corresponding positions, then vertical equality applies
Two parallel lines are cut by a transversal. A co-interior pair sits between the lines on the same side of the transversal. One angle is 80 degrees and the other is marked (2x + 20) degrees. What is x?
Answer: ______________
Two parallel lines are cut by a transversal. Two co-interior angles sit between the lines on the same side of the transversal. One measures 115°. What is the other?
- 115°
- 65°
- 75°
Two parallel lines are cut by a transversal. At one intersection, an interior angle measures 48°. Its co-interior angle at the other intersection sits between the lines on the same side of the transversal. Type its measure in degrees.
Answer: ______________
Two parallel lines are cut by a transversal. A corresponding pair is marked (3x + 20) degrees and (x + 60) degrees. Find x and their common measure, then find the co-interior partner of the interior member of that pair. What is that partner in degrees?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

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Alternate angles · A Z-shape marks alternate interior angles. They sit between the parallel lines on opposite sides of the transversal.
Two 90 degree angles · Co-interior angles add to 180 degrees. An equal pair sums to twice its size. Only 90 + 90 = 180, so only the two 90 degree angles can be co-interior.
180 · Co-interior angles sit between parallel lines on the same side of the transversal. For parallel lines they always add to 180 degrees, whatever the individual measures are.
Corresponding angles · An F-shape marks corresponding angles: they sit in matching corners at each crossing and are equal.
4x + 2x = 180 · Co-interior angles add to 180 degrees, so the two expressions must sum to 180: 4x + 2x = 180.
Translation matches corresponding positions, then vertical equality applies · A translation along the transversal preserves ray directions, so it maps one parallel line onto the other and carries each angle onto its corresponding partner. The alternate interior angle is vertically opposite that partner, and vertically opposite angles are equal.
40 · Co-interior angles add to 180 degrees, so 80 + (2x + 20) = 180. Combining gives 2x + 100 = 180, then 2x = 80, so x = 40. The marked angle is 2(40) + 20 = 100 degrees, and 80 + 100 = 180.
65° · Co-interior angles add to 180° when the lines are parallel, so the other angle is 180° - 115° = 65°.
132 · Co-interior angles add to 180° when the lines are parallel, so 180° - 48° = 132°.
100 · Corresponding angles are equal, so 3x + 20 = x + 60. Subtracting x and 20 gives 2x = 40, so x = 20. The common measure is 3(20) + 20 = 80 degrees. The co-interior partner is 180 - 80 = 100 degrees.