Worksheet: Inscribed Angles in a Circle

In this worksheet, we will practice identifying theorems about inscribed angles, including theorems that state angles subtended by the same arc are equal and the angle subtended by an arc at the center is double the angle subtended at the circumference.

Q1:

Given that and , determine the value of .

Q2:

Given that , and , find , and .

• A , ,
• B , ,
• C , ,
• D , ,

Q3:

From the figure, what is ?

Q4:

Given that , find , and .

• A , ,
• B , ,
• C , ,
• D , ,

Q5:

Find the value of .

Q6:

The measure of is . Find .

Q7:

Given that , find .

Q8:

Given that , find .

Q9:

In the given figure, the diameter of circle is . If , what is ?

• A
• B
• C
• D

Q10:

Given that is a diameter in the circle , and , find in degrees.

Q11:

Find .

Q12:

Given that and , find .

Q13:

Find and .

• A ,
• B ,
• C ,
• D ,

Q14:

Given that , find .

Q15:

Given that , find .

Q16:

Given that is a diameter of the circle and , find .

Q17:

In the figure, is the center of the circle, and is the nonreflex angle at . Given that , find .

Q18:

Given that , find .

Q19:

Given that , and , find and .

• A ,
• B ,
• C ,
• D ,

Q20:

Find .

Q21:

Find .

Q22:

In the figure, intersects the circle at and , and intersects the circle at and . Given that , find .

Q23:

If the measure of an arc of a circle is , what is the measure of the inscribed angle subtended by that arc?

Q24:

Find .

Q25:

In the figure, is the center and .

What is the measure of angle ?

What is the measure of angle ?