Reflex Angles

We have been learning about measuring angles lately, specifically reflex angles. A reflex angle is any angle greater than 180 degrees. Before teaching about measuring these angles, however, we reviewed the three main types of angles: acute, obtuse and right angles.

We then learned about benchmark angles. I explain that a right angle is a good helper when we are estimating angles, and then if we cut a right angle in half, then we know it is a 45 degree angle. On the other side, if we split the difference between a 90 degree and a 180 degree angle, a good benchmark is a 135 degree angle. These can help us to estimate any angle that we see within a reasonable amount.

The reason I often insist on students estimating angles before measuring them is because many students make the error of reading the wrong side of the protractor when they measure. For example, they may measure a 60 degree angle, but call it a 120 degree angle because they looked at the wrong number for their reading. If they estimate first, it can help students to recognize that they have done this. Here is a game to practice estimating angles:

Banana Hunt

To measure a reflex angle, we looked at an acute angle first, and then examined the angle on the other side, which is the reflex angle (see diagram).

Next, I ask students if they see the shape that the acute and reflex angles make. If you join the two, you will see that it makes a circle, or a 360 degree angle. All angles have this, so to find the reflex angle, all we do is measure the inside angle, then subtract from 360! Here is a video that helps explain this. It shows another way to measure reflex angles as well:

Finally, here is a webpage that reviews reflex angles and has a few questions for practice:

Reflex Angles