Circle Angles Exploration

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Circle with central and inscribed angles

📐 Part 1: Identifying Circle Angles

1. Which angle is a central angle?

An angle with its vertex on the circumference

An angle with its vertex at the centre of the circle

An angle formed by two chords

An angle formed by a tangent and radius

2. If a central angle measures 80°, what is the measure of an inscribed angle subtending the same arc?

80°

40°

160°

20°

3. Circle all the properties that apply to inscribed angles:

Vertex is on the circumference

Vertex is at the centre

Measure is half the central angle subtending the same arc

Both arms are radii

4. A central angle measures 120°. Calculate the inscribed angle subtending the same arc.

Inscribed angle = _______ ÷ _______ = _______°

🔍 Part 2: Problem Solving

5. In a circle, an inscribed angle measures 35°. What is the measure of the central angle subtending the same arc?

6. Two inscribed angles subtend the same arc. If one measures 42°, what is the measure of the other inscribed angle? Explain your reasoning.

7. A central angle measures 150°. Find:

a) The inscribed angle subtending the same arc: _______°

b) The reflex central angle: _______°

c) An inscribed angle subtending the reflex arc: _______°

8. Explain the relationship between central and inscribed angles in your own words:

⭐ Part 3: Extension Challenge

9. Advanced: In a circle, three points A, B, and C are on the circumference. If the central angle BOC is 100°, find the inscribed angle BAC.

10. Creative Challenge: Draw a circle and mark:

• A central angle of 60°

• An inscribed angle subtending the same arc

• Label all vertices and write the angle measures

11. Real-world Connection: Describe a situation where you might encounter central or inscribed angles in everyday life:

Circle Angles Exploration

Circle Angles Exploration

📐 Part 1: Identifying Circle Angles

🔍 Part 2: Problem Solving

⭐ Part 3: Extension Challenge

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