MathsFreePrintable
Circle Angles Exploration
A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.
Circle Angles Exploration
📐 Part 1: Identifying Circle Angles
1. What is a central angle?
An angle with its vertex at the centre of the circle
An angle with its vertex on the circumference
An angle formed by two chords
An angle measuring 90 degrees
2. What is an inscribed angle?
An angle with its vertex at the centre of the circle
An angle with its vertex on the circumference
An angle inside a square
An angle measuring 180 degrees
3. If a central angle measures 80°, what is the measure of an inscribed angle subtending the same arc?
80°
40°
160°
20°
4. Which parts of a circle can form the arms of a central angle? (Select all that apply)
Radii
Chords
Diameters
Tangents
🔢 Part 2: Calculating Circle Angles
5. A central angle measures 120°. Calculate the inscribed angle that subtends the same arc.
Answer: The inscribed angle measures _______°
6. An inscribed angle measures 35°. What is the measure of the central angle subtending the same arc?
Answer: The central angle measures _______°
7. In a circle, if an inscribed angle subtends an arc of 140°, what is the measure of the inscribed angle?
Answer: The inscribed angle measures _______°
8. Extension Challenge: If two inscribed angles subtend the same arc, what can you conclude about their measures? Explain your reasoning.
🎯 Part 3: Problem Solving & Reasoning
9. Draw and label a circle showing both a central angle and an inscribed angle that subtend the same arc. Label all important parts.
10. Explain in your own words the relationship between central and inscribed angles that subtend the same arc.
11. Real-world Connection: A clock face is a circle. If the hour hand moves from 12 to 4, what central angle does it create? If you were standing on the edge of a giant clock face, what would be the inscribed angle?
Central angle: _______° Inscribed angle: _______°
12. Advanced Challenge: In a circle, if an inscribed angle measures x°, write an algebraic expression for the central angle that subtends the same arc.
Central angle = _____________
About This Worksheet
Free in Kuraplan
Sign up free, grab the PDF, and customize it for your class.
Print-Ready
Formatted for standard paper. Clean layout, easy to read.
AI-Generated
Created with Kuraplan's AI, designed for real classroom use.
For Teachers & Parents
Use in classrooms, for homework, tutoring, or homeschool.
Need a custom version of this worksheet?
Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.
Generate Custom Worksheets — Free No credit card Curriculum-aligned Under 60 seconds
