Study guides › Level 7 · Geometry

Angles in a circle

Level 7 · Geometry · for questions like “An angle at the center of a circle is 100°. An angle at the edge opens onto the same arc. How big is it?”

💡 The idea

• An angle at the edge is half the angle at the center when both open onto the same arc.
• In a four-sided shape with all corners on the circle, opposite angles add to 180°.
• An angle in a semicircle (opening onto a diameter) is always 90°.

🪜 The steps

1. Find which angle is at the center and which is at the edge.
2. Halve, or double, as needed.

✏️ Worked examples

1. Center 100°: the edge angle is 50°.

2. Edge 35°: the center angle is 70°.

3. Four corners on the circle, one angle 110°: the opposite angle is 70°.

⚠️ Watch out

• The center angle is always the bigger one.

🎯 Try these

1. Center 84°: edge angle?
2. Edge 40°: center angle?
3. Four corners on a circle, one angle 95°: opposite angle?

Answers: 1) 42° 2) 80° 3) 85°

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