- 213 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about 'lesson 8-5' - ostinmannual

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Central Angle

Definition:

An angle whose vertex lies on the center of the circle.

NOT A Central Angle

(of a circle)

Central Angle

(of a circle)

Central Angle

(of a circle)

Lesson 8-5: Angle Formulas

110

110

O

Z

Central Angle TheoremThe measure of a center angle is equal to the measure of the intercepted arc.

Center Angle

Intercepted Arc

Example:

Give is the diameter, find the value of x and y and z in the figure.

Lesson 8-5: Angle Formulas

Example: Find the measure of each arc.

4x + 3x + (3x +10) + 2x + (2x-14) = 360°

14x – 4 = 360°

14x = 364°

x = 26°

4x = 4(26) = 104°

3x = 3(26) = 78°

3x +10 = 3(26) +10= 88°

2x = 2(26) = 52°

2x – 14 = 2(26) – 14 = 38°

Lesson 8-5: Angle Formulas

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).

Examples:

3

1

2

4

Yes!

No!

No!

Yes!

Lesson 8-5: Angle Formulas

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

The measure of an inscribed angle is equal to ½ the measure of the intercepted arc.

Y

Inscribed Angle

110

55

Z

Intercepted Arc

An angle formed by a chord and a tangent can be considered an inscribed angle.

Lesson 8-5: Angle Formulas

F

A

°

°

40

y

D

°

50

B

°

°

y

50

B

°

x

C

°

C

x

E

E

Examples: Find the value of x and y in the fig.

Lesson 8-5: Angle Formulas

D

1

B

C

Interior Angle TheoremDefinition:

Angles that are formed by two intersecting chords.

2

E

Interior Angle Theorem:

The measure of the angle formed by the two intersecting chords is equal to ½ the sum of the measures of the intercepted arcs.

Lesson 8-5: Angle Formulas

1

y

°

2

y

°

°

x

3

x

°

y

°

x

Exterior AnglesAn angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle.

Two secants

2 tangents

A secant and a tangent

Lesson 8-5: Angle Formulas

Exterior Angle Theorem

The measure of the angle formed is equal to ½ the difference of the intercepted arcs.

Lesson 8-5: Angle Formulas

Example: Exterior Angle Theorem

Lesson 8-5: Angle Formulas

If a quadrilateral is inscribed in a circle, then the opposite angles are supplementary.

mDAB + mDCB = 180

mADC + mABC = 180

Lesson 8-5: Angle Formulas

Download Presentation

Connecting to Server..