Investigation 3: Measuring and Drawing Angles with a Protractor
A protractor measures angles in degrees by aligning its center hole with the angle vertex and its baseline along one ray, then reading the degree mark where the second ray intersects the curved scale. In Grade 6 Saxon Math Course 1 (Chapter 3: Number, Operations, and Geometry), students learn to place the protractor correctly, choose the correct scale (inner or outer), and read values accurately. Most protractors have two scales: inner and outer. Use the scale that starts at 0° on the ray you aligned. Acute angles measure less than 90°, right angles exactly 90°, and obtuse angles between 90° and 180°.
Key Concepts
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: $$m\angle AOB = 45^{\circ}$$ 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.
Common Questions
How do you use a protractor to measure an angle?
Place the center hole on the vertex. Align the baseline with one ray. Read the degree mark where the second ray crosses the curved scale, choosing the scale that begins at 0° on the aligned ray.
Why do protractors have two scales?
Two scales (inner and outer) allow measurement from either direction. Always use the scale where 0° aligns with the ray you placed along the baseline.
What is the difference between an acute, right, and obtuse angle?
Acute: less than 90°. Right: exactly 90°. Obtuse: greater than 90° but less than 180°.
How do you draw an angle of 65° using a protractor?
Draw a ray. Place the protractor center on the ray endpoint and baseline along the ray. Mark the 65° point on the scale. Draw a second ray from the endpoint through that mark.
A student reads 115° on one scale and 65° on the other. Which is correct for an obtuse angle?
115° is correct. Obtuse angles exceed 90°, so 115° (obtuse) is the right reading. 65° would indicate an acute angle.