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MathidiaMathematics Academy
Angle reasoning and constructions
Lesson 41 of 75
Introduction

Angles in parallel lines

Objective. Use corresponding, alternate and co-interior angle facts.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Angles in parallel lines are created when a straight transversal crosses two parallel lines, producing equal or supplementary angle pairs at each intersection. Corresponding angles are equal and sit in matching positions, alternate angles are equal and sit on opposite sides of the transversal between the lines, and co-interior angles sum to 180°. If one angle is 65°, its corresponding angle is also 65°, while its co-interior angle on the same side is 180° − 65° = 115°. Always identify the angle pair type correctly before deciding whether to use equality or add to 180°.

Worked example

Two parallel lines are cut by a transversal. One angle is 72°, and its co-interior angle is marked x. Find angle x.

72
Illustrated card showing 72
  1. 1Recall that co-interior angles sum to 180°
  2. 2Write the equation: x + 72 = 180
  3. 3Subtract 72 from both sides: x = 180 − 72
  4. 4The value of x is 108°

Answer: 108°

Concept mastery

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Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

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Common mistake. Pupils frequently assume all angle pairs formed by parallel lines are equal, wrongly setting co-interior angles equal instead of summing them to 180°. Always check the angles' positions to distinguish co-interior pairs from corresponding or alternate pairs.

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