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Circle Angles Exploration

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Circle Angles Exploration

Use the circle-angle relationships to solve each problem. Show calculations for questions that ask you to find an angle, and include degree symbols in your answers.

Explore the relationships

In a circle, a central angle has its vertex at the centre. An inscribed angle has its vertex on the circumference. Angles subtended by the same arc are related: the inscribed angle is half the central angle. Two inscribed angles subtending the same arc are equal.

1.A circle has centre O, and B and C are points on its circumference. Which angle has its vertex at the centre O?

2.A central angle and an inscribed angle subtend the same arc. If the central angle is 86°, what is the inscribed angle?

43°
86°
172°
94°

3.Fill in the blanks: An inscribed angle subtending a given arc is the central angle subtending that same arc.

Solve the angle puzzles

For each problem, use the fact that the central angle is twice the inscribed angle when both subtend the same arc. Angles around a point total 360°.

4.An inscribed angle subtending arc PQ is 37°. Find the central angle subtending arc PQ. Show the calculation.

5.Two inscribed angles, ∠PRQ and ∠PSQ, subtend the same arc PQ. If ∠PRQ = 51°, find ∠PSQ and explain why.

6.The smaller central angle XOY is 148°. Find the reflex angle XOY. Then find an inscribed angle subtending the major arc XY.

7.In a circle, central angle AOB is 4x° and inscribed angle ACB subtending the same minor arc AB is (x + 30)°. Find x and both angle measures.

8.An inscribed angle subtending a diameter is always a right angle. Decide whether this statement is true or false, and give a reason.

TrueFalse

9.For angles subtending the same arc, state the ratio of the central angle to the inscribed angle. If the inscribed angle is 28°, use the ratio to find the central angle.

10.Draw a circle with centre O and choose two points P and Q on its circumference. Add a third point R on the circumference so that ∠POQ = 100°. Label ∠PRQ and write its measure, making sure it subtends the same minor arc PQ.

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Year 7

Circle Angles Exploration

Circle Angles Exploration

Explore the relationships

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2 printable pages

About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

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