Practice Central Angle in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An angle whose vertex is at the center of a circle, with its two rays intersecting the circle at two points. Its measure equals the measure of the intercepted arc.
Imagine standing at the center of a clock face. The angle between the hour and minute hands is a central angle. The arc between the two numbers the hands point to is the intercepted arc, and its measure (in degrees) equals the angle you see.
Example 1
easyA central angle in a circle intercepts an arc of 130°. What is the measure of the central angle?
Example 2
mediumIn a circle, three central angles divide the circle into three arcs with measures 3x°, 5x°, and 4x°. Find each arc and central angle.
Example 3
easyA circle is divided into 6 equal sectors. What is the central angle of each sector?
Example 4
hardIn circle O, central angle AOB = 80° and central angle BOC = 110°. Find arc AC going the short way (not through B), and the reflex arc AC going through B.