# 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?

• A
• B
• C
• D

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 ?