Lesson 1.4: Measure and Classify Angles

• An angle consists of two different rays with the same endpoint.

• The rays are the sides of the angle.

• The endpoint is the vertex of the angle.

Ex. 1: Write 3 names for the angle shown. Then name the vertex and sides of the angle.

A

B C

Ex.2: Name the three angles in the diagram.

Classifying Angles:

Angles can be classified as acute, right, obtuse, and straight.

• Acute angles have a measure greater than 0 and less than 90.

• Right angles have a measure of 90.

• Obtuse angles have a measure greater than 90 and less than 180.

• Straight angles have a measure of 180.

Measuring Angles:

• A protractor can be used to approximate the measure of an angle.

• An angle is measured in units called degrees (o).

Postulate 3 Protractor Postulate:

The measure of is equal to the absolute value of the difference between the real numbers for and .

OB��������������

OA��������������

AOB

A

O B

EXAMPLE 3 Measure and classify angles

Use the diagram to find the measure of the indicated angle. Then classify the angle.

a. <GHL b. <JHK b. <GHK c. <GHJ

Postulate 4 Angle Addition Postulate:

If P is in the interior of , then

m RST m RSP m PST

RST

Ex 4 and 5: Find the indicated angle measure.

26°

76°

m < QST = _____

Q R

S T

51°

m < QST = _____

A

B

C D

Ex.6: Given that , find and

.

145om LKN m LKMm MKN

Ex.7: Given that is a straight angle,

find and .

KLMm KLN m NLM

Ex.8: Given that is a right angle, find

and .

EFG

m EFH m HFG

Congruent Angles:

Two angles are congruent angles if they have the same measure.

Ex.9: Use the diagram below.

a. Identify all pairs of congruent angles.

b. Given that , ,and

Find the other angle measures in the diagram.

121om TSR

84om QRS 130om PQR

Ex 10: Find the indicated angle measure.

a°

b°

c°

103°

e°d°

48°

f°

1. a°

2. b°

3. c°

4. d°

5. e°

6. f°

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

Ex.11: In the diagram below, bisects , and . Find the other two angle measures not given. .

018m XYW XYZYW

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In the diagram BD bisects <ABC.

Find m < ABC.

A

D

C

B

(5x-11)° (4x+1)°

Homework

Pgs 28-30 #1, 3-10, 15-31, 33-38, 40-42