# 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 1 ∘ 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:

Jackson 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