# Worksheet: Central Angles in a Circle

In this worksheet, we will practice identifying a central angle in a circle and finding its measure using its properties.

Q1:

In the given figure, the circle has center and radius 7 cm. Given that , find , rounded to the nearest tenth, and .

• A ,
• B ,
• C ,
• D ,

Q2:

How many angles are in a circle?

Q3:

How many turns are needed to make a complete turn?

Q4:

How many angles does it take to make a full turn?

Q5:

Jacob turns one-third of a full turn. How many degrees is this?

Q6:

This circle is divided into 3 equal parts. What is the angle of each part?

Q7:

What is the value of the central angle of a circular sector when a circular segment and a circular sector have the same area?

Q8:

Find .

Q9:

, , and are three points on a circle with radius 54 cm and center . The point is the intersection of and and we have and . Find the central angle of the major circular segment giving the answer to the nearest second.

• A
• B
• C
• D

Q10:

A circle has a circumference of units. Find, in degrees, the measure of the central angle of an arc with a length of units.

Q11:

In the figure, given that the circumference is 96 and , find .

Q12:

What is the measure of half a circle?

Q13:

Circle has radius 32 and . Determine and to the nearest hundredth.

• A , 56.50
• B , 28.25
• C , 16.97
• D , 15.03

Q14:

In the given figure, the circle has center and radius 9.9 cm. Given that , find , rounded to the nearest tenth, and .

• A ,
• B ,
• C ,
• D ,

Q15:

In the given figure, the circle has center and radius 8.5 cm. Given that , find , rounded to the nearest tenth, and .

• A ,
• B ,
• C ,
• D ,

Q16:

The given figure shows a circle with center .

Which of the following is a central angle?

• A
• B
• C
• D
• E

Which of the following is an inscribed angle?

• A
• B
• C
• D
• E

Which of the following is a circumscribed angle?

• A
• B
• C
• D
• E