In this video, I will help show you how to correctly draw angles. First, we need to review a bit about angles and their measures. Remember, an angle is merely two rays that share an endpoint. If you look at the examples below, the common point in each stands out, and the arrows represent rays that share that point. An angle measure is given between 0 degrees and 360 degrees. In most cases angles are referred to as acute, between zero and ninety degrees, right, ninety degrees exactly, or obtuse, between ninety and one hundred eighty degrees. There are two other names for angles you might see in this class. Straight angles are angles that measure exactly one hundred eighty degrees; they look like a straight line. And reflex angles are angles between one hundred eighty and three hundred sixty degrees. Pause the video and identify which types of angles are shown below. Check your work in a moment by resuming playback… Do your answers match? Make sure you understand why each angle was described like this before moving on. In addition to the types of angles, in this module we identified both positive and negative angles. Positive angles are measured counter-clockwise from the base of the angle, and negative angles are measured clockwise from the base of the angle. If the base of an angle is not given, then we can assume the angle measure is supposed to be positive.

When it comes to drawing angles, make sure you follow the steps listed here. We will use them in our examples next… Example one…Draw an angle that measures thirty-seven degrees. Start by centering your protractor at the vertex, and then align the protractor's base with the base ray. Around the curve of the protractor, mark the thirty-seven degree angle. The thirty-seven degree mark is two ticks past thirty-five when counting up from zero. Be careful not to mark this angle from the wrong side of the protractor. Finally, remove the protractor and connect the vertex with the mark you made at thirty-seven degrees. To double check our work, I'll allow the computer to show the angle measure. It shows thirty-seven degrees just as we intended. Now example two…

Draw an angle that measures negative one hundred twenty degrees. Start by centering your protractor at the vertex, and then align the protractor's base with the base ray. Since this is a negative angle, I want the next ray that I draw to be in a clockwise position from this base ray. I need to align the protractor like this, this time. Around the curve of the protractor, mark the one hundred twenty degree angle. Be careful not to mark this angle from the wrong side of the protractor. Finally, remove the protractor and connect the vertex with the mark you made. To double check our work, I'll allow the computer to show the angle measure. It shows negative one hundred twenty degrees just as we intended.

We did not cover how to draw reflex angles in this video, though doing so is not much more difficult. Since a reflex angle is an angle greater than one hundred eighty degrees, it's easy to draw a straight angle first, and measure from it the difference between the reflex angle measure and one hundred eighty degrees. For example, if I wanted to draw an angle that measures two hundred ten degrees, I would recognize it is thirty degrees beyond one hundred eighty. I could lightly draw a straight angle, and measure thirty degrees beyond it to complete the two hundred ten degree angle. Give that a try on your own. I'll show you what your end result will look like when you resume playback of this video in just a moment… Here is an angle measuring two hundred ten degrees. It is thirty degrees beyond one hundred eighty.

Please be sure to practice these techniques on your own. Make sure you can draw both positive and negative angles, both acute and obtuse. And try your hand at drawing reflex angles as well. Good luck!