Degrees: Measuring Angles

We measure the size of an angle using degrees. Example: Here are some examples of angles and their degree measurements.

ProtractorA device used to measure angles.

Reading a ProtractorWhich side of a protractor scale do you use?

•The easiest way to decide which scale to use is to look at the angle you're measuring. •If it is greater than a right angle (more than ninety degrees)

then use the scale that has numbers greater than 90.•If the angle is less than a right angle (measures less than 90 degrees), use the scale which has numbers less than 90. •Of course you have to line up the protractor correctly with

the center point on the vertex of the angle and one of the rays of the angle coincide with the line on the protractor. Happy measuring!

Measuring, calculating and drawing angles...

Our learning objectives today

To use a protractor to:a) measure acute and obtuse angles to the

nearest degree.b) draw acute and obtuse angles to the nearest

degree.To calculate angles on a straight line.

What do we use to help us?A protractor

These are standard protractors.

When we use a protractor, we need to line it up correctly with the angle.

You need to make sure the protractor is lined up correctly.

Is this ready to measure the angle?

Were you right?............it

wasn’t!

Look for the upside down ‘T’ in the middle of the straight line on your protractor.

In this protractor look for the hole in the

center.

These spots need to be exactly on the vertex of your angle.

We also need to remember to line up the base

One side of the angle must be lined up with the base of the protractor.

It doesn’t matter which side.

What does it measure?

This angle measures 35°.

Acute Angles

An acute angle is an angle measuring between 0 and 90 degrees.

Examples:

                                                               

Obtuse Angles

An obtuse angle is an angle measuring between 90 and 180 degrees.

Example:

                                                                 

Right Angles

A right angle is an angle measuring 90 degrees, exactly.

Examples:

                                      

A perigon (or a revolution) is an angle that equals exactly 360º.

Reflex Angle

A reflex angle is greater than 180º and less than 360º. It represents the largest amount of rotation.

Now, we will use a protractor to measure the reflex angle PQR.

Measuring Reflex Angles

To measure the reflex angle PQR, extend the arm PQ to A to form angle PQA which is a straight angle.  Then

measure the size of the angle AQR and add

180º.

Angle Bisector

The bisector of an angle, also called the angle

bisector is the ray, line or line segment that divides the angle into two equal

parts.

.D

Complementary AnglesTwo angles are called complementary angles if the sum of their degree measurements equals 90 degrees.

Example:

These two angles are complementary. Their sum is 90˚.

                                                      

58° + 32° = 90°

These two angles can be "pasted" together to form a right angle! Adjacent complementary angles.

Complementary Angles

Supplementary AnglesTwo angles are called supplementary angles if the sumof their degree measurements equals 180 degrees.

Example: These two angles are supplementary. The sum of their measures is 180˚

                                                                      

139° +41° = 180 °

Two angles that share a vertex and a side to form a line.

Two angles that can be "pasted" together to form a straight line!

Linear Pair of AnglesSpecial Supplementary Angles

Vertical AnglesOpposite angles formed by intersecting lines .     

For any two lines that meet, such as in the diagram below, angle AEB and angle DEC are called vertical angles. Angle BEC and angle AED are also vertical angles. Vertical angles are congruent - have the same degree measurement.          

Review

State whether the following are acute, right, or obtuse.1.

2.

3.

4.

5.

??

acute obtuseright

obtuseacute

Complementary and Supplementary

1. Two angles are complementary. One measures 65 degrees.

2. Two angles are supplementary. One measures 140 degrees.

Find the missing angle.

Answer : 25

Answer : 40

Complementary and Supplementary

Find the missing angle. You do not have a protractor.Use the clues in the pictures.

1.2.x

55 165x

x = 90° – 55° x = 180° – 165°

x = 35 ° x = 15°

Vertical Angles

Find the missing angle. You do not have a protractor.

Use the clues in the pictures.

58x

x = 58

More drawings

20

C

J

D

E F

G

H

70

9070

20

90 Box in the corner indicates a right angle.

Final Drawing

52

B

A

F E

D

C

60

G

68

686052