### Measuring Angles

We measure a line segment’s *length* with a ruler. Angles are measured with something called a **protractor**. A protractor is a measuring device that measures how “open” an angle is. Angles are measured in degrees, and labeled with a

Notice that there are two sets of measurements, one opening clockwise and one opening counter-clockwise, from

For every angle there is a number between

The **Angle Addition Postulate** states that if

#### Drawing a 50∘ Angle with a Protractor

- Start by drawing a horizontal line across the page, about 2 in long.
- Place an endpoint at the left side of your line.
- Place the protractor on this point. Make sure to put the center point on the bottom line of the protractor on the vertex. Mark
50∘ on the appropriate scale. - Remove the protractor and connect the vertex and the
50∘ mark.

#### Copying an Angle with a Compass and Straightedge

- We are going to copy the angle created in the previous investigation, a
50∘ angle. First, draw a straight line, about 2 inches long, and place an endpoint at one end. - With the point (non-pencil side) of the compass on the vertex, draw an arc that passes through both sides of the angle. Repeat this arc with the line we drew in #1.
- Move the point of the compass to the horizontal side of the angle we are copying. Place the point where the arc intersects this side. Open (or close) the “mouth” of the compass so you can draw an arc that intersects the other side of the arc drawn in #2. Repeat this on the line we drew in #1.
- Draw a line from the new vertex to the arc intersections.

#### Measuring Angles

Measure the three angles using a protractor.

It might be easier to measure these three angles if you separate them. With measurement, we put an

#### Using a Protractor

What is the measure of the angle shown below?

This angle is not lined up with

Using the inner scale,

Using the outer scale,

#### Using the Angle Addition Postulate

What is

Using the Angle Addition Postulate,

#### Drawing an Angle

Draw a

Following the steps from above, your angle should look like this:

### Examples

#### Example 1

Use a protractor to measure

The easiest way to measure any angle is to line one side up with

#### Example 2

What is

From the Angle Addition Postulate,

#### Example 3

If

From the Angle Addition Postulate,

So,

### Review

1. What is

2. If

For questions 3-6, determine if the statement is true or false.

- For an angle
∠ABC,C is the vertex. - For an angle
∠ABC,AB¯¯¯¯¯¯¯¯ andBC¯¯¯¯¯¯¯¯ are the sides. - The \begin{align*}m\end{align*} in front of \begin{align*}m \angle ABC\end{align*} means measure.
- The Angle Addition Postulate says that an angle is equal to the sum of the smaller angles around it.

For 7-12, draw the angle with the given degree, using a protractor and a ruler.

- \begin{align*}55^\circ\end{align*}
- \begin{align*}92^\circ\end{align*}
- \begin{align*}178^\circ\end{align*}
- \begin{align*}5^\circ\end{align*}
- \begin{align*}120^\circ\end{align*}
- \begin{align*}73^\circ\end{align*}

For 13-16, use a protractor to determine the measure of each angle.

Solve for \begin{align*}x\end{align*}.

- \begin{align*}m\angle ADC = 56^\circ\end{align*}
- \begin{align*}m \angle ADC = 130^\circ\end{align*}
- \begin{align*}m \angle ADC = (16x - 55)^\circ\end{align*}
- \begin{align*}m \angle ADC = ( 9x - 80)^\circ\end{align*}

### Review (Answers)

To view the Review answers, open this PDF file and look for section 1.5.