Finding Inscribed Angle Measures
When working with inscribed angles in circles, remember that an inscribed angle equals half the measure of its intercepted arc. This relationship helps solve many circle problems.
The problems on this page ask you to find various angle and arc measures within circles. For example, when you know an arc measure equals 176°, the inscribed angle that intercepts that arc would measure 88°. Similarly, if you know an inscribed angle measures 31°, the arc it intercepts would measure 62°.
Some problems require you to work with multiple angles and arcs in the same circle. In these cases, remember that angles in the same segment of a circle are equal, and a central angle equals twice the inscribed angle that intercepts the same arc.
Pro Tip: When solving for variables in circle problems, set up equations using the relationships between inscribed angles and their arcs. The inscribed angle is always half the measure of its intercepted arc!
The second half of this page introduces problems where you need to find the value of x in expressions like or that represent angle or arc measures. To solve these, you'll need to create equations using circle properties and then solve for x.
