Lesson 8-5: Angle Formulas 1 Bell Ringer 5/27/2010 Find the value of x.

Lesson 8-5: Angle Formulas 2 Central Angle (of a circle) Central Angle (of a circle) NOT A Central Angle (of a circle) Central Angle An angle whose vertex lies on the center of the circle. Definition:

Lesson 8-5: Angle Formulas 3 Inscribed Angle Inscribed Angle: An angle whose vertex lies on a circle and whose sides are chords of the circle (or one side tangent to the circle) No! Yes! Examples:

Lesson 8-5: Angle Formulas 4 Intercepted Arc Intercepted Arc: An angle intercepts an arc if and only if each of the following conditions holds: 1. The endpoints of the arc lie on the angle. 2. All points of the arc, except the endpoints, are in the interior of the angle. 3. Each side of the angle contains an endpoint of the arc.

Lesson 8-5: Angle Formulas 5 Inscribed Angle Theorem The measure of an inscribed angle is equal to ½ the measure of the intercepted arc. Y Z 55  110  Inscribed Angle Intercepted Arc An angle formed by a chord and a tangent can be considered an inscribed angle.

Lesson 8-5: Angle Formulas 6 Examples: Find the value of x and y in the fig. y  40  x  50  A B C D E y  x   A B C E F

Lesson 8-5: Angle Formulas 7 An angle inscribed in a semicircle is a right angle. R P 180  S 90 

Lesson 8-5: Angle Formulas 8 Find the value of x and y.

Lesson 8-5: Angle Formulas 9 Inscribed Quadrilaterals m  DAB + m  DCB = 180  m  ADC + m  ABC = 180  If a quadrilateral is inscribed in a circle, then the opposite angles are supplementary.

Lesson 8-5: Angle Formulas 10 Find the value of z and y.

Lesson 8-5: Angle Formulas 11 Homework Page 617 #9-26