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Warm up. 30 . 8 0 . 100 . 180 . 100 . 260 . Wheel of Formulas!!. Central Angle. Angle = Arc. Inscribed Angle. Angle where the vertex is ON the circle. Inscribed Angle. 160 . The arc is twice as big as the angle!!. 80 . Find the value of x and y. 120 . . 120 . x.

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Warm up
Warm up

30

80

100

180

100

260



Central angle
Central Angle

Angle = Arc


Inscribed angle
Inscribed Angle

  • Angle where the vertex is ON the circle



160

The arc is twice as big as the angle!!

80


Find the value of x and y.

120

120

x

60

y


Examples

J

K

Q

S

M

Examples

1. If mJK= 80 and JMK = 2x – 4, find x.

x = 22

2. If mMKS= 56, find m MS.

112


Find the measure of DOG and DIG

D

72˚

G

If two inscribed angles intercept the same arc, then they are congruent.

O

I



Q circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.uadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY

B

A

D

C


diameter


Q circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

D

3

J

T

4

U

Example 3

In J, m3 = 5x and m 4 = 2x + 9.

Find the value of x.

x = 3


Example 4 circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.

4x – 14 = 90

H

K

x = 26

N

G


Example 5 Find y and z. circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

z

110

110 + y =180

y

y = 70

85

z + 85 = 180

z = 95


Practice ws
Practice WS circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

10 problems


Homework ws
Homework WS circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

6.4 Practice


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