Reading the Correct Scale
Reading the correct scale on a protractor prevents a common error caused by the two sets of numbers printed on every protractor. In Grade 6 Saxon Math Course 1, students first classify the angle as acute (less than 90°) or obtuse (greater than 90°), then select the scale that gives a reading consistent with that classification. An acute angle must read less than 90° and an obtuse angle must read between 90° and 180°. This classification check makes scale selection unambiguous.
Key Concepts
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!
Common Questions
Why does a protractor have two sets of numbers?
Protractors can be used from either direction, so both scales (0–180 going each way) are printed. You read the scale that starts at zero on the ray you placed at 0°.
How do you decide which scale to read?
First classify the angle as acute (< 90°) or obtuse (> 90°). Then choose the scale that gives a reading matching that classification.
An angle looks acute. Both scales give 35° and 145°. Which is correct?
35°, because it is less than 90° and matches the acute classification.
What is the first step when measuring an angle with a protractor?
Place the center point of the protractor on the angle's vertex and align the zero mark with one ray.
What angle type gives a reading between 90° and 180°?
An obtuse angle. Always verify: if the angle visually opens wider than a right angle, the reading must be greater than 90°.