Investigation 3: Measuring and Drawing Angles with a Protractor

New Concept

Angles are measured in units called degrees ($^{\circ}$) using a protractor. The formal notation for stating an angle's measure is shown below.

We write "the measure of angle AOB is $45^{\circ}$" as:

What’s next

This card introduces the core idea of angle measurement. Next, you'll tackle practice problems on both measuring existing angles and drawing new ones with a protractor.

Property

A protractor has two sets of numbers. To ensure you are reading the correct scale, first decide if the angle is acute (less than $90^{\circ}$) or obtuse (greater than $90^{\circ}$). Then, read the number from the scale that matches the type of angle you are measuring.

Examples

An angle's ray points to both 50 and 130 on the scales. Since the angle is clearly acute, its correct measure is $50^{\circ}$.
Another angle's ray lands between 110 and 70. Because the angle is wide and obtuse, its correct measure must be $110^{\circ}$.
If you measure an angle from the left zero mark and the other ray passes 45, you use the inner scale; if measuring from the right, you use the outer scale.

Explanation

Ever notice your protractor has two rows of numbers? Don't panic! It's just so you can measure from the left or the right. Before you measure, just ask: is this a small, acute angle or a big, obtuse one? Pick the number that makes sense. A tiny angle is never going to be 160 degrees!

Property

A protractor is a tool to measure angles in units called degrees. Place the center point of the protractor on the vertex of the angle and a zero mark on one ray. Where the other ray passes through the scale, we read the degree measure. We write the measure of angle AOB as $m\angle AOB = 45^{\circ}$.

Examples

To measure $\angle XYZ$, place the protractor's center on vertex $Y$ and the zero line on ray $YX$. If ray $YZ$ passes through 60, then $m\angle XYZ = 60^{\circ}$.
If an angle is obtuse, like $\angle PQR$, its measure will be greater than $90^{\circ}$. You might read 120 on the protractor, so $m\angle PQR = 120^{\circ}$.
A right angle, such as $\angle LMN$, will line up perfectly with the $90^{\circ}$ mark on the protractor, meaning $m\angle LMN = 90^{\circ}$.

Explanation

Think of a protractor as a ruler for angles! Instead of inches, it measures in degrees. Just line up the center hole with the angle's corner (the vertex) and an arm with the zero line. The number that the other arm points to is the angle's size. It’s a simple way to give every angle a precise number!

Property

To draw an angle, first draw a ray. Position the protractor's center point on the endpoint of the ray and a zero degree mark on the ray. Then, make a dot on the paper at the appropriate degree mark. Finally, remove the protractor and draw a ray from the endpoint of the first ray through the dot.

Examples

To draw a $75^{\circ}$ angle, draw a ray, place the protractor's center on the endpoint, find the $75^{\circ}$ mark, make a dot, and connect it.
To draw a $140^{\circ}$ obtuse angle, follow the same steps but be sure to make your dot at the $140^{\circ}$ mark, not the $40^{\circ}$ mark.
To construct a perfect $90^{\circ}$ right angle, place your dot precisely at the $90^{\circ}$ mark before drawing the second ray to form the corner.

Explanation

Want to be an angle artist? It's like following a recipe! Start with a line, which is your base. Plop the protractor's center on the end and line it up with zero. Find your target number, make a dot, and then connect it back to the start. You've just drawn a perfect angle. You're a geometry chef!