Do Now One-half of the measure of an angle plus the angle’s supplement is equal to the measure of the angle. Find the measure of the angle.

10.5 Apply Other Angle Relationships in Circles Objective: To find the measures of angles inside or outside a circle

Theorem If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc. B C 1 2 A

Examples:

Theorem: Angle Inside Circle If two chords intersect inside a circle, then the measure of each angle is one half the sum of the arcs intercepted by the angle and its vertical angle. D A 1 2 C B

Theorem: Angles Outside Circle If two lines intersect a circle at one or two points, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs. B A 1 C

Theorem: Angles Outside Circle P Q 2 R X W 3 Z Y

Examples

Examples