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.
Name:Date:
Circle Angles Exploration
Use the angle facts to solve each problem. Show working for calculations and include degree symbols in your answers.
Angle facts
A central angle has its vertex at the centre of the circle. An inscribed angle has its vertex on the circumference. When they subtend the same arc, the central angle is twice the inscribed angle.
1.A central angle and an inscribed angle subtend the same arc. If the inscribed angle is 35°, what is the central angle?
2.A central angle subtending a particular arc is 86°. Find the inscribed angle subtending that same arc.
3.An inscribed angle subtending an arc is 37°. Calculate the central angle subtending the same arc.
4.At a hardware store, Hana tests a circular display fixture. Two sight lines from a point on its edge meet the ends of the same arc as a 118° central angle. What angle do Hana’s sight lines make?
5.Oliver measures an inscribed angle of 42° on a circular sign. Freya measures another inscribed angle subtending the same arc. What should Freya measure, and why?
6.A circular clock face has 12 equal divisions. The hour hand turns from 12 to 4, making a central angle. Find that angle, then find an inscribed angle subtending the same arc.
7.A central angle is labelled (3x + 12)° and an inscribed angle subtending the same arc is labelled (x + 8)°. Find x and both angle measures.
8.A central angle and an inscribed angle subtend the same arc. The central angle is 156°. A student says the inscribed angle is 78°. Is the student correct? Explain using the angle relationship.
9.Draw a circle with centre O. Mark points A and B on the circumference and point C elsewhere on the circumference. Draw and label central angle AOB and inscribed angle ACB so they subtend the same minor arc AB.
2 printable pages
Page 1
Page 2
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
More Maths Worksheets
Year 7
Proportion and Ratios Worksheet
Free
Year 4
Probability Vocabulary Exploration
Free
Year 8
Formulae Exploration Worksheet
Free
Year 9
Integer Operations Practice
Free
Year 10
Tessellation Pattern Exploration
Free
Year 3–4
Basic Probability Exploration
Free
Year 7
Time Duration Problem Cards
Free
Year 4