GEOMETRY INSCRIBED ANGLES Unit 6-2

Central angles A __________ ____________ is an angle whose vertex is at the center of a circle with sides that are radii of the circle. An ______________ __________ consists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them. A chord or arc ____________ an angle if its endpoints lie on the sides of the angle. Central Angle Intercepted Arc Subtends

Inscribed Angles An __________ ____________ is an angle whose vertex is on a circle and whose sides contain chords of the circle. InscribedAngle The measure of a central angle is _____________ to the measure of the intercepted arc The measure of an inscribed angle is _____________ of the measure of the intercepted arc. Equal Half

Central Angles A B C 80 o What is the intercepted arc? (highlight the arc) What is the angle? What is the measure of the angle?

Inscribed Angles

B A C The measure of the inscribed angle is equal to half of the measure of the intercepted arc. 60 o 120 o 156 o 78 o

Examples Find R U P S 27 o 118 o Find

Examples E D C A 64 o Find B

Examples x C A (8z – 6) o Find x B

Inscribed quadrilaterals If a quadrilateral is inscribed inside of a circle, then the opposite angles are supplementary A B C D

Examples G J K (3b+25) o Find b H (10b-69) o (6b+20) o

Examples Find a