Most protractors are in the form of a semicircle, marked off into 180 degrees, every ten degrees being numbered as 0, 10, 20, 30, etc. The marking usually goes from left to right, just the way an angle moves through an arc, but many protractors have a reverse scale beneath the main one, this reverse scale reading from right to left. There is also a vertical line in the center of the base. We'll call this line X.



Suppose that you are required to draw an angle of 37 degrees to the horizontal. The first thing to do is to draw the horizontal line, with a vertical line cutting it in O. Now carefully place the base of the protractor on this horizontal line so that the line X on the protractor coincides with the point O, and the horizontal line passes through the 0 degree and 180 degrees of the protractor.

If this is done correctly, the vertical line will pass through the 90-degree mark. Now, holding the protractor firm with the left hand, make a small point mark at the 37-degree line on the protractor.

It will be just two medium-length lines above the 35-degree point. Call this point A. Now remove the protractor and connect point O with A by drawing a straight line through O and A. This line will be 37 degrees to the horizontal. Note that the protractor is divided into half degrees, and each space from 0 to 10, or from 10 to 20, etc., is divided into 10 medium line spaces, and 20 short line spaces, with the 5 line longer than the rest.

To draw any angle to any line at a given point, merely place the base of the protractor on the line so that the line X is at the given point, making sure that the line passes through the 0 and 180-degree mark of the protractor. Then mark off the required angle on the rim of the protractor, remove the protractor and join this point with the point on the given line by means of a straight line. This line will be at the required angle to the given line.

Exercises:

1. Draw the following angles to a horizontal line:

14, 25, 39, 47, 54, 68, 77, 81 degrees

2. Draw the following angles to a vertical line:

16, 33, 49, 66, 71, 80 degrees

3. To any line drawn at any angle, draw a line at 48 degrees to the line at any point.

4. The base of a triangle is 3 inches long. The angle at the left is 124 degrees, and the left side is also 3 inches. What are the other two angles?

With some practice, the use of the protractor will become second nature.