1. Warm-up
Find the measure of each arc

2. Table of Contents 41. Inscribed Angles

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

4. 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

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

6. Example A
mABD = ?
98o
196o C B D

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

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

9. Example
Find m Y W
55o Y X C Z

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

11. 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

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

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