Inscribed Angles Worksheet Solutions for Easy Learning

Inscribed Angles Worksheet Solutions for Easy Learning

Inscribed angles are a fundamental concept in geometry, and understanding how to solve problems related to them is crucial for students. In this article, we will provide inscribed angles worksheet solutions to help students learn and practice this concept easily.

What are Inscribed Angles?

Inscribed angles are angles whose vertices lie on a circle and whose sides are chords of the circle. The angle formed by these chords is called an inscribed angle. Inscribed angles are also known as circular angles.

Properties of Inscribed Angles

Before we dive into the worksheet solutions, let’s review some key properties of inscribed angles:

• The measure of an inscribed angle is half the measure of its intercepted arc.
• Inscribed angles that intercept the same arc are congruent.
• Inscribed angles that intercept congruent arcs are congruent.

Inscribed Angles Worksheet Solutions

Here are some worksheet solutions to help you practice and learn about inscribed angles:

Problem 1: Find the measure of the inscribed angle ∠ABC, given that the measure of the intercepted arc AB is 60°.

Solution:

The measure of an inscribed angle is half the measure of its intercepted arc. Therefore, the measure of ∠ABC is half of 60°, which is 30°.

Problem 2: In the diagram, ∠PQR and ∠STR are inscribed angles that intercept the same arc. If the measure of ∠PQR is 45°, what is the measure of ∠STR?

Solution:

Since inscribed angles that intercept the same arc are congruent, ∠PQR and ∠STR are congruent. Therefore, the measure of ∠STR is also 45°.

Problem 3: Find the measure of the inscribed angle ∠JKL, given that the measure of the intercepted arc JL is 120°.

Solution:

The measure of an inscribed angle is half the measure of its intercepted arc. Therefore, the measure of ∠JKL is half of 120°, which is 60°.

Problem 4: In the diagram, ∠MNO and ∠PQR are inscribed angles that intercept congruent arcs. If the measure of ∠MNO is 30°, what is the measure of ∠PQR?

Solution:

Since inscribed angles that intercept congruent arcs are congruent, ∠MNO and ∠PQR are congruent. Therefore, the measure of ∠PQR is also 30°.

Notes

📝 Note: Make sure to identify the intercepted arc and the inscribed angle correctly to solve problems related to inscribed angles.

Conclusion

Inscribed angles are an essential concept in geometry, and understanding how to solve problems related to them is crucial for students. By practicing with these worksheet solutions, students can develop a deeper understanding of inscribed angles and their properties. Remember to always identify the intercepted arc and the inscribed angle correctly to solve problems related to inscribed angles.