Angles and their Measurements

Delaine Sanders

www.flicr.com/photos/34669486/N00/40234362

Angle Parts

http://www.flickr.com/photos/dcab2/3514913853/

Angle Parts

http://www.flickr.com/photos/dcab2/3514913853/

2 Rays and a Vertex

Angle Parts

.B

B

A

B

C

RAY BC →

RAY BA →

POINT B

BC

BA

Angle Parts

C

A

B

2

Angle Naming

B

ABC

CBA

2

A

B

C

2

Angle Naming

A

B

C

D

12

Angle Naming

ADB or BDA

BDC or CDB

ADC or CDA

1

2

A

B

C

D

12

Angle Naming Practice (STOP)

A

BC

D

E

F

G

Measuring Angles

Degrees

The angle is the amount ofrotation from one ray to the other ray.

Measuring Angles

protractor

Measuring Angles

protractor

Measuring Angles

50

50 – 0 = 50m = 50

protractor

Measuring Angles

130

130 – 0 = 130

m = 130

Measuring Angles

50

50 – 0 = 50

180 – 130 = 50

Measuring Angles (STOP)

Measuring Angles Practice – image on note sheet

Note sheet, clear protractors and 6 inch rulers

Paper Practice Measure side angle Measure corner angle Fold in half, measure corner angle

0° - 90°

                                                               

Acute Angles

Acute Angles

http://www.flickr.com/photos/24418961@N05/3524410992/

Acute Angles

90° - 180°

                                                              

   

Obtuse Angles

Obtuse Angles

http://www.flickr.com/photos/enlightenedfellow/1578956556/

Obtuse Angles

= 90°

                                      

Right Angles

Right Angle

http://www.flickr.com/photos/jefemontana/2317256019/

Right Angle

http://www.flickr.com/photos/jefemontana/2317256019/

Straight Angle

= 180 °

.

Straight Angle

http://www.flickr.com/photos/forevermoosed/469130102/

http://www.flickr.com/photos/bolivar-trindade/3203862834/

Straight Angle

Interior / Exterior Point

. A

E

C

D

F .

Interior / Exterior Point

. A

E

C

D

Point A is interior to DEC

Point F is exterior to DEC

Ray EA is interior to DEC

F .

Angle Addition Postulate

The sum of the two smaller angles will always equal the measure of the larger angle.

R

M K

W

Angle Addition Postulate

The sum of the two smaller angles will always equal the measure of the larger angle.

R

M K

W

m MRK + m KRW = m MRW

Angle Addition Postulate

2

1

1 + 2 = ABC

A

B C

Angle Addition Postulate

2

1

1 = 30 – 0 = 30

2 = 70 – 30 = 40

ABC = 30 + 40 = 70

A

B C

Angle Addition Postulate

http://www.flickr.com/photos/svyates/2415340942/

12

Angle 1 = 2x

Angle 2 = x

Solve for angle 1

Angle Bisector

An angle bisector is a ray that divides an angle into two equal angles.

A

B

C

E

ABC CBE

m ABC = m CBE

Bisected Angle

http://www.flickr.com/photos/40256716@N00/367560012/

Bisected Angle

http://www.flickr.com/photos/40256716@N00/367560012/

Bisected Angle

Ray UK bisects angle U. What is the measure of angle U?

j41°

41°

64

U

K