# Worksheet: Measures of Arcs

In this worksheet, we will practice finding measures of arcs based on the measures of central and inscribed angles.

Q1:

Given that is a diameter in circle and , determine . Q2:

Which of these is equal to the measure of an arc?

• Athe measure of the central angle subtended by that arc
• Bthe inscribed angle subtended by that arc

Q3:

Find the measure of the arc that represents of the circumference of a circle.

Q4:

Given that is a diameter in circle of center and , determine . Q5:

An arc measures of the circumference of a circle. What angle does the arc subtend at the center?

Q6:

Suppose that . Determine . Q7:

What is ? Q8:

Find and . • A,
• B,
• C,
• D,

Q9:

and are two points on a circle center so that the measure of is of that of its reflex angle. What is the minor arc ?

Q10:

Given that and , find . Q11:

Given that measure arc the measure of arc , find . Q12:

Find . Q13:

An arc has a measure of .

What is the measure of the central angle?

What is the measure of the inscribed angle?

What is the measure of the circumscribed angle?

Q14:

Given that is a diameter in circle and , determine . Q15:

Given that is a diameter in circle and , determine . Q16:

Find the measure of the arc that represents of the circumference of a circle.

Q17:

Given that is a diameter in circle of center and , determine . Q18:

Given that is a diameter in circle of center and , determine . Q19:

Given that is a diameter in circle of center and , determine . Q20:

If , what is ? Q21:

Given that , find , and . • A, ,
• B, ,
• C, ,
• D, ,

Q22:

Find the value of . Q23:

Given that , find . Q24:

In the given figure, which of the following would represent the minor arc passing through and ? • A
• B
• C
• D
• E