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# Warm up PowerPoint PPT Presentation

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.

Warm up

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30

80

100

180

100

260

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

60

y

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

• If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

Quadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY

B

A

D

C

• If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.

diameter

Q

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

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.

z

110

110 + y =180

y

y = 70

85

z + 85 = 180

z = 95

10 problems

6.4 Practice