Section 1-4: Measuring Angles

Objective: Find the measurement of angles using the Angle Addition Postulate

AngleFormed by two rays with the same endpoint.

Rays

Vertex(endpoint)

Naming Angles

Name the Rays of the angle:

What is the vertex of the angle? Vertex is B

1

Different ways to name the angle: • Name by vertex:• Name by 3 points (vertex in middle):• Name by a number:

Geometry is used to construct roofs. Use the diagram below to answer the following questions.

F

G

H

1 2

What is the vertex of the large angle?

Name all the angles in the diagram using both letters & numbers.

Name the Rays of the angle:

The vertex is G

I

Protractor PostulateFor every angle, there corresponds a number between 0 and 180º. This number is called the measure of the angle and is written in degrees.

Postulate 1-7

Measuring Angles and the Protractor Postulate

Four Different Classifications of Angles

Right Angle Straight Angle

Acute Angle Obtuse Angle

Using a Protractor to Measure Angles

1. Place the vertex at zero on the protractor2. Align one ray with the bottom edge of the protractor3. Read measurement (in degrees) on protractor4. Caution:

Pay attention to the numbersEnsure answer makes sense

What type of angle is represented in the diagram?

Angle Addition PostulatePostulate 1-8

Angle Addition Postulate

If the mDEG = 145º , find the mGEF.

D E F

G

145º + _____ = 18035

AXB and BXD form linear pairs and are adjacent angles

Name the adjacent angles? Are they a linear pair?

Use the Angle Addition Postulate to solve.

m 1 + m 2 = m ABC Angle Addition Postulate.

42 + m 2 = 88 Substitute 42 for m 1 and 88 for m ABC.

m 2 = 46 Subtract 42 from each side.

Suppose that m 1 = 42 and m ABC = 88. Find m 2.

What postulate do you use to solve the problem?