Central and inscribed angles worksheet answer key pdf

Central Angles: Angles with the vertex located at the center of the circle. The measure of the central angle is the same as the measure of the arc it intercepts. Inscribed Angles: Angles with the vertex located on the circumference of the circle.

Example 1: By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. The measure of the central angle ∠POR of the intercepted arc ⌢PR is 90°. Therefore, m∠PQR=12m∠POR =12(90°) =45°.

In a circumference, the measure of the central angle that subtends the same arc of any inscribed angle is twice the measure of any inscribed angle that subtends the same arc.

Identifying Arc Angle Indicated An arc angle's measurement is shown as m⌢AB m A B ⌢ where A and B are the two points on the circle creating the arc. The m means measurement, and the short curved line over the ⌢AB A B ⌢ indicates we are referring to the arc.