Central Angles Worksheet
A Grade 12 Math worksheet focusing on understanding and calculating central angles in circles, their relationship to arcs and chords.
Includes
Standards
Topics
Central Angles
Name:
Date:
Score:
Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. What is the definition of a central angle?
An angle whose vertex is on the circle.
An angle whose vertex is the center of the circle.
An angle whose vertex is outside the circle.
An angle formed by two tangents.
2. If a central angle measures 90 degrees, what is the measure of its intercepted arc?
45 degrees
180 degrees
90 degrees
360 degrees
3. The measure of a central angle is equal to the measure of its .
4. A chord that subtends a central angle of 180 degrees is a of the circle.
5. In a circle with center O, if arc AB measures 120 degrees, what is the measure of central angle AOB? Explain your reasoning.
6. A central angle can be larger than 360 degrees.
True
False
7. The arcs intercepted by congruent central angles in the same circle are congruent.
True
False
8. A circle has a radius of 10 cm. A central angle intercepts an arc with a length of 5π cm. Calculate the measure of the central angle in degrees. Show all your steps.