Geometry 1-3Geometry 1-3

Measuring and Constructing Measuring and Constructing AnglesAngles

VocabularyVocabulary

• Angle- a figure formed by two rays, or sides, with a common endpoint.

• Vertex- The common endpoint of an angle (plural: vertices).

• Interior of an angle- all points between the sides of an angle.

• Exterior of an angle- all points outside of the sides of an angle.

• Degree- the unit of measure for angles.

Naming AnglesNaming Angles

• Angles can be named three ways:1. By its vertex R

2. By a number 1

3. By a point on each ray and the vertex SRT or TRS

S

RT

1

Name the Marked AngleName the Marked Angle

A R L

W

2

• Acute angle: 1° to 89 °

• Right angle: 90 °

• Obtuse angle: 91 ° to 179 °

• Straight angle: 180 °

Types of AnglesTypes of Angles

More Vocab.More Vocab.

• Congruent angles- angles that have the same measure.

• Angle bisector- A ray that divides an angle into two congruent angles

Congruent angles:

ARW LRWAngle bisector: RW

A

R L

W

45°45°

PostulatePostulate

• Angle Addition Postulate:If S is in the interior of PQR, then

m PQS + m SQR = m PQR

(part 1 + part 2 = the whole)

R

Q

S

P

ExampleExample

• What is the measure of angle WRL?

A

R L

WT

45°65°

ExampleExample

• If Y is in the interior of LMN, find the

m LMY if m LMY = 5x+3, m YMN = 3x+3, and m LMN=86°.

Using a ProtractorUsing a Protractorwxv zxwYXZ