Central Angle Worksheet
A Grade 9 math worksheet focusing on understanding and calculating central angles in circles, including their relationship with arcs and chords.
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Central Angle Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for calculation problems.
1. What is a central angle?
An angle whose vertex is on the circle.
An angle whose vertex is the center of the circle.
An angle formed by two chords.
An angle formed by a tangent and a chord.
2. The measure of a central angle is equal to the measure of its .
inscribed angle
intercepted arc
major arc
diameter
3. In the circle with center O, if m∠AOB = 75°, what is the measure of arc AB?
4. If a central angle measures 120 degrees, what fraction of the circle's circumference does its intercepted arc represent?
5. A central angle is an angle formed by two of a circle.
6. The sum of all central angles in a circle is degrees.
7. A central angle is always smaller than an inscribed angle that intercepts the same arc.
True
False
8. If two central angles in the same circle are congruent, then their intercepted arcs are also congruent.
True
False
9. A circle has a radius of 10 cm. If a central angle measures 90°, what is the length of the intercepted arc?
10. In a circle, two central angles, ∠XOY and ∠YOZ, are adjacent. If m∠XOY = 40° and m∠XOZ = 100°, what is the measure of ∠YOZ?