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Inscribed Angles - Worksheet 8 - 10th Grade

Hard

Apply the inscribed angle theorem and corollaries (Hard)

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

About This Worksheet

This hard-level worksheet contains 27 problems designed for 10th Grade students practicing inscribed angles. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

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: In a cyclic quadrilateral one angle measures 66°. Find the opposite angle.
Solution Steps:
  1. A cyclic quadrilateral has all four vertices on a circle.
  2. Its opposite angles are supplementary.
  3. 180 - 66 = 114°.
Answer: 114°
Tip: This follows from the inscribed angle theorem — the two arcs together make the full 360°.
1
In a cyclic quadrilateral, one angle measures 33°. Find the opposite angle.
2
In a cyclic quadrilateral, one angle measures 45°. Find the opposite angle.
3
In a cyclic quadrilateral, one angle measures 39°. Find the opposite angle.
4
An inscribed angle intercepts a semicircle. Find the angle.
5
In a cyclic quadrilateral, one angle measures 124°. Find the opposite angle.
6
In a cyclic quadrilateral, one angle measures 131°. Find the opposite angle.
7
An inscribed angle intercepts a semicircle. Find the angle.
8
In a cyclic quadrilateral, one angle measures 44°. Find the opposite angle.
9
An inscribed angle intercepts a semicircle. Find the angle.
10
In a cyclic quadrilateral, one angle measures 89°. Find the opposite angle.
11
An inscribed angle intercepts a semicircle. Find the angle.
12
In a cyclic quadrilateral, one angle measures 51°. Find the opposite angle.
13
An inscribed angle intercepts a semicircle. Find the angle.
14
An inscribed angle intercepts a semicircle. Find the angle.
15
An inscribed angle intercepts a semicircle. Find the angle.
16
In a cyclic quadrilateral, one angle measures 74°. Find the opposite angle.
17
In a cyclic quadrilateral, one angle measures 115°. Find the opposite angle.
18
In a cyclic quadrilateral, one angle measures 136°. Find the opposite angle.
19
In a cyclic quadrilateral, one angle measures 115°. Find the opposite angle.
20
An inscribed angle intercepts a semicircle. Find the angle.
21
An inscribed angle intercepts a semicircle. Find the angle.
22
In a cyclic quadrilateral, one angle measures 39°. Find the opposite angle.
23
In a cyclic quadrilateral, one angle measures 96°. Find the opposite angle.
24
An inscribed angle intercepts a semicircle. Find the angle.
25
An inscribed angle intercepts a semicircle. Find the angle.
26
In a cyclic quadrilateral, one angle measures 45°. Find the opposite angle.
27
An inscribed angle intercepts a semicircle. Find the angle.

Answer Key

1. 147°2. 135°3. 141°4. 90°5. 56°6. 49°7. 90°8. 136°9. 90°10. 91°11. 90°12. 129°13. 90°14. 90°15. 90°16. 106°17. 65°18. 44°19. 65°20. 90°21. 90°22. 141°23. 84°24. 90°25. 90°26. 135°27. 90°

Frequently Asked Questions

How do I download this inscribed angles - worksheet 8 worksheet?

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How do I find worksheets at different difficulty levels?

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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 27 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.