Students will learn to compare angles, understand the 360-degree system, and correctly read a protractor using both inner and outer scales.
Concept of rotation and degrees.
How do we know if one angle is larger than another? The size of an angle is simply the amount of rotation or turn needed to move the first ray to the position of the second ray about the vertex.
Imagine opening a book cover: the wider you open it, the greater the rotation, and the larger the angle formed!
Divisible by almost all numbers
360 is the smallest number that can be evenly divided by almost every number from 1 to 10 (except 7)! It can be divided evenly into 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, and 24 parts. This made calculations without modern calculators incredibly convenient for ancient mathematicians.
Image of a labeled protractor measuring an angle.
Align the center mark with the vertex and the 0° line with the base arm.
Introduction to the protractor and its two scales.
To measure an angle in degrees, we use a tool called a protractor. A standard protractor is a semi-circle divided into 180 equal parts, allowing us to measure angles from to .
Worked example analyzing an incorrect protractor reading.
A student is measuring an angle, . They place the center of the protractor on the vertex and align the right-pointing arm with the baseline. Looking at where the other arm points, they read the number on the protractor and confidently state: .
However, is visibly an obtuse angle (greater than ). What went wrong?
Faded example on finding angle difference.
When measuring angles with a protractor, we usually align one arm with the zero line. However, we can also determine an angle's measure directly from any two marks on the scale. Suppose an angle has arm OT passing through the mark and arm OS passing through the mark.
To find the measure of , we calculate the difference between these two points. We do this by setting up the subtraction: - = .
Therefore, the total angle measure is . This method saves time compared to counting each unit of 1 degree individually.
MCQ testing scale selection.
You place a protractor on an angle. The base arm aligns with the mark on the OUTER scale (pointing to the left). The other arm passes through the mark that says on the outer scale and on the inner scale. What is the measure of the angle?