Inscribed Angles - Worksheet 1 - 10th Grade

Easy

Apply the inscribed angle theorem and corollaries (Easy)

18 problems · 20-25 minutes · Skills: circles, inscribed angles, geometry

About This Worksheet

This easy-level worksheet contains 18 problems designed for 10th Grade students practicing inscribed angles. Easy worksheets use simpler numbers and straightforward problem types to build confidence and reinforce foundational skills.

The Inscribed Angle Theorem is one of the most elegant and useful results in circle geometry. It connects angles and arcs in a precise way that enables problem solving throughout circle geometry and appears in higher mathematics including the geometry of complex numbers and the unit circle in trigonometry.

  • Apply the Inscribed Angle Theorem (inscribed angle = half the intercepted arc)
  • Use corollaries to find angles inscribed in semicircles or in the same arc
  • Apply the properties of inscribed polygons, especially cyclic quadrilaterals
  • Calculate angles formed by two chords intersecting inside a circle
  • Solve for missing arc or angle measures in multi-step circle diagram problems

How to Solve: Worked Example

Example Problem: An inscribed angle intercepts an arc of 112°. Find the angle.
Solution Steps:
  1. The Inscribed Angle Theorem: the angle is half its intercepted arc.
  2. 112 ÷ 2.
  3. = 56°.
Answer: 56°
Tip: Inscribed angle = half the arc. The vertex sits on the circle, not at the centre.
1
An inscribed angle intercepts an arc of 112°. Find the inscribed angle.
2
An inscribed angle intercepts an arc of 140°. Find the inscribed angle.
3
An inscribed angle intercepts an arc of 30°. Find the inscribed angle.
4
An inscribed angle intercepts an arc of 104°. Find the inscribed angle.
5
An inscribed angle intercepts an arc of 74°. Find the inscribed angle.
6
An inscribed angle intercepts an arc of 72°. Find the inscribed angle.
7
An inscribed angle intercepts an arc of 38°. Find the inscribed angle.
8
An inscribed angle intercepts an arc of 108°. Find the inscribed angle.
9
An inscribed angle intercepts an arc of 88°. Find the inscribed angle.
10
An inscribed angle intercepts an arc of 78°. Find the inscribed angle.
11
An inscribed angle intercepts an arc of 172°. Find the inscribed angle.
12
An inscribed angle intercepts an arc of 22°. Find the inscribed angle.
13
An inscribed angle intercepts an arc of 108°. Find the inscribed angle.
14
An inscribed angle intercepts an arc of 80°. Find the inscribed angle.
15
An inscribed angle intercepts an arc of 160°. Find the inscribed angle.
16
An inscribed angle intercepts an arc of 104°. Find the inscribed angle.
17
An inscribed angle intercepts an arc of 126°. Find the inscribed angle.
18
An inscribed angle intercepts an arc of 30°. Find the inscribed angle.

Answer Key

1. 56°2. 70°3. 15°4. 52°5. 37°6. 36°7. 19°8. 54°9. 44°10. 39°11. 86°12. 11°13. 54°14. 40°15. 80°16. 52°17. 63°18. 15°

Frequently Asked Questions

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What skills does this circles worksheet cover?

This worksheet focuses on circles, inscribed angles, geometry. It is designed for 10th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 18 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.