Study guides › Level 7 · Geometry

Angles and parallel lines

Level 7 · Geometry · for questions like “Two parallel lines are crossed by a third line. One angle is 70°. How big is its alternate interior angle?”

💡 The idea

When a line crosses two parallel lines, it makes the same angles at both crossings. Every angle is either equal to a given one or adds to 180° with it.

🪜 The steps

• Equal:

- corresponding angles, in the same spot at each crossing (an F shape);

- alternate interior angles, inside the parallels on opposite sides (a Z shape).

• Add to 180°: same-side interior angles, inside the parallels on the same side (a C or U shape).

✏️ Worked examples

1. One angle is 70°. Its alternate interior angle? Equal: 70°.

2. One angle is 70°. Its same-side interior angle? 180 − 70 = 110°.

⚠️ Watch out

• Sketch it. Two lines, a slanted line across, then label the angles.
• Sharp angles go with sharp, wide with wide. A sharp angle and a wide angle add to 180°.

🎯 Try these

1. One angle is 55°. Its corresponding angle?
2. One angle is 125°. Its same-side interior angle?
3. One angle is 80°. Its alternate interior angle?

Answers: 1) 55° 2) 55° 3) 80°

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.