Measuring and Drawing Angles

Angles are all around us! In geometry, we measure angles in degrees (symbolized as $^\circ$). To measure and draw angles accurately, we use a tool called a protractor.

How to Measure an Angle

A protractor looks like a half-circle with numbers from $0$ to $180$ along the curved edge. Here is how to use it:

1. Place the center of the protractor directly over the vertex (the point) of the angle.
2. Line up the base line of the protractor with one of the lines of the angle so it points exactly at $0^\circ$.
3. Read the number where the second line of the angle crosses the curved edge of the protractor. Make sure to use the correct scale (inner or outer) that starts at zero on your base line!

How to Draw an Angle

Let's say you need to draw a $75^\circ$ angle. Just follow these steps:

1. Use a ruler to draw a straight base line. Draw a dot on one end to be the vertex.
2. Place the center of the protractor on your vertex dot, and align the $0^\circ$ mark with your base line.
3. Find $75^\circ$ on the protractor's scale and make a small mark on your paper.
4. Remove the protractor and use a straight edge to draw a line connecting the vertex to your mark. You've just drawn a $75^\circ$ angle!

Finding Missing Angles

Sometimes, you don't even need a protractor to find an angle's measurement.

A straight line is always exactly $180^\circ$. If a straight line is split into two smaller angles, those two angles must add up to $180^\circ$.

Example: Two angles sit side-by-side to form a straight line. If one angle is $120^\circ$, what is the size of the other angle?

We know the total is $180^\circ$. Let the unknown angle be $x$. $120^\circ + x = 180^\circ$

To find $x$, subtract the known angle from $180^\circ$: $x = 180^\circ - 120^\circ = 60^\circ$

The missing angle is $60^\circ$.