Warm-up Find the measure of each arc

Table of Contents 41. Inscribed Angles

Inscribed angles Standard – MM2G3 – Understand properties of circles Essential Question – What are the properties of inscribed angles?

Definitions Inscribed angle- an angle whose vertex is on a circle and whose sides are chords of the circle. Intercepted arc- the arc that the inscribed angle makes B BCD  ( BD A  C D

Formula The measure of an inscribed angle is ½ the measure of its intercepted arc. mBAC= ½ m BC B A C (

Example A mABD = ? 98o 196o C B D

Example x = ? 70 = ½ 7x Or 7x = 140 B 70o A x=20 C ( m AD = ? 7xo 140o

Example – sometimes what is asked for is not in line with given information……. B x = ? xo A 360-100-120=240 C x=1/2(240)=120 120o D

Example Find m Y W 55o Y X C Z

Ex: find x. P PQ is a diameter,  R is a rt. . 3x = 900 x = 30 3xo R C Q

Quadrilaterals in a circle If a quadrilateral is inscribed in a circle, the opposite angles are supplementary. A mA + mC = 180o mB +mD = 180o D B C

Ex: x=? and y=? 85 + x = 180 x = 95 80 + y = 180 y = 100 yo xo 85o 80o

Assessment 321 Name 3 properties of inscribed angles Name 2 rules about inscribed polygons Name 1 question you have about this material