To measure angles using a protractor.

To draw angles using a protractor.

Different types of angles

In geometry, angles are measured in units called

_______.degrees

The symbol for degree is °.

Q

P

R75°

In the figure below, the angle is 75 degrees.

Now, let’s measure an angle using a protractor.Now, let’s measure an angle using a protractor.

Q

R S

Use a protractor to measure SRQ.

1) Place the center point of the protractor on vertex R. Align the straightedge with side RS.

2) Use the scale that begins with 0 at RS. Read where the other side of the angle, RQ, crosses this scale.

1200

J

H

G

SQ R

m SRQ =

Find the measurement of:

m SRJ =

m SRG =

180

45

150

Let’s measure the following Let’s measure the following angles.angles.

J

H

G

SQ R

m QRG =

m GRJ =

70

180 – 150= 30

150 – 45= 105

m SRH ≈

Let’s measure an anglesLet’s measure an angles

Use a protractor to draw an angle having a measure of 135.

1) Draw AB

2) Place the center point of the protractor on A. Align the mark labeled 0 with the ray.

3) Locate and draw point C at the mark labeled 135. Draw AC.

C

A B

Try this one.Try this one.

acute angle:less than 900

Lets look at some Lets look at some angles.angles.

right angle: 900

obtuse angle:more than 900

straight angle: 1800

Classify each angle as acute, obtuse, or right.

110°

90°40°

50°

130° 75°

Obtuse

Obtuse

Acute

Acute Acute

Right

5x - 7

B

The measure of B is 138.Solve for x.

B = 5x – 7 and B = 138

Given: (What do you know?)

5x – 7 = 138

5x = 145

x = 295(29) -7 = ?

145 -7 = ?

138 = 138

Check!

Let’s use Algebra to answer the following.

Here’s another one.

9y + 4H

The measure of H is 67.Solve for y.

H = 9y + 4 and H = 67

Given: (What do you know?)

9y + 4 = 67

9y = 63

y = 79(7) + 4 = ?

63 + 4 = ?

67 = 67

Check!

ba

Is m a larger than m b ?

60° 60°

1) Draw an acute, an obtuse, or a right angle. Label the angle RST.

R

TS

2) Draw and label a point X in the interior of the angle. Then draw SX.

X

3) For each angle, find mRSX, mXST, and RST.

30°

45°

75°

Let’s try something different.

congruent angles:

Here are some more Here are some more types of angles.types of angles.

vertical angles: opposite angles

adjacent angles:

Determine whether 1 and 2 are adjacent angles.

No. They have a common vertex B, but _____________

no common side1 2

B

12

G

Yes. They have the same vertex G and a common side with no interior points in common.

N

1

2J

L

No. They do not have a common vertex or ____________a common side

The side of 1 is ____LN

JNThe side of 2 is ____

Here are some questions.

Determine whether 1 and 2 are adjacent angles.

No.

21

Yes.

1 2

X D Z

In this example, the noncommon sides of the adjacent angles form a___________.straight line

These angles are called a _________linear pair

Let’s try something different.

Find the value of x in the figure:

The angles are vertical angles.

So, the value of x is 130°.

130°

x°

Let’s try something different.

Find the value of x in the figure:

The angles are vertical angles.

(x – 10) = 125.

(x – 10)°

125°

x – 10 = 125.

x = 135.

Let’s try something different.

Assignment

1.6 Measuring AnglesGeometry

5. If m1 = 2x + 3 and the m3 = 3x + 2, then find the m3

6. If mABD = 4x + 5 and the mDBC = 2x + 1, then find the mEBC

7. If m1 = 4x - 13 and the m3 = 2x + 19, then find the m4

8. If mEBG = 7x + 11 and the mEBH = 2x + 7, then find the m1

A B C

D

E

G

H

12

34

Draw the following angles.

1. 500 2. 750 3. 1350 4. 1150

? ? ?? ? ?