Angles

Which of these two pencils is the pointiest? The left one, right? But how much pointier is it? One centimeter pointier? One kilogram?

One square meter? How do you even measure pointiness? This is about angles. An angle measures how far a line is rotated in relation to another line. Pick a point.

Draw a line straight out from the point - a ray, to use the correct word. Draw another ray from the same point, but in a different direction. When talking of angles, we call these two rays sides. To measure the rotation between these two sides, we need a scale to measure on. Angles are measured in degrees, like this.

The scale looks a bit like a face of a clock, but instead of one turn being 60 minutes, one turn is 360 degrees. Degrees have their own symbol, a small raised ring. Both the symbol and the word "degree" are recognized when we talk about temperature. But here it means something other than degrees Celsius. An angle degree is one 360th of a turn.

Since a whole turn is 360 degrees, half a turn is 180 degrees. A quarter of a turn is half of half turn, 90 degrees. And three quarters of a turn is three quarters of 360. In other words, 270 degrees. Look at the angle that we drew earlier.

One angle is at side, and the other, right between 0 and 90 degrees. The angle is 45 degrees. A 45 degree angle. When we have a scale, we can measure these two pencils' points. We start with the blunt one.

The angle's point should be at the middle of the scale, and one angle side or one edge of the pencil's point against zero on the scale. We can now read the scale by the second angle side, or the other side of the pencil's point. The pencil's point angle is 50 degrees. So, let us compare it to the other pencil. Put it in the same way - point in the middle, one side against zero, and read it.

This one is only 30 degrees. A lower number of degrees means a pointier angle. This pencil is 20 degrees pointier than the other. If you draw a scale like this on a round clear piece of plastic, you get a protractor. A protractor is good to have when measuring angles.

Put the center point against the tip of the angle, and turn it until you have one of the angle's sides against zero. You can then read how many degrees is the angle by looking at the number the second side ends. But be alert - make sure you measure the right angle. If you hold the degree disc wrongly, you will measure the rest of the turn. To mark the angle mean - the inner and outer - draw a small bow in the angle, like this.

Since it is 60 degrees, we mean this angle and not 300. Sometimes it is enough to get an approximate angle. There are some terms to remember in order to do that. Since this angle is smaller than 90 degrees, we call it acute. If we increase the angle to exactly 90 degrees, it is no longer acute, but a right angle.

Look at the little bow. Here it has become a lower case L. This means that it is just that - a right angle. This is an obtuse angle. All angles that are larger than 90 but smaller than 180 degrees are obtuse.

Now the angle is completely straight. You cannot even see that it is an angle anymore. One angle side points towards the opposite direction of the other. This angle is exactly 180 degrees. If we make the angle even bigger, it becomes overly obtuse, or a reflex angle.

You won't encounter reflex angles as often as the other types. To measure an angle it is good to have a protractor. There are round protractors and those that are only semi-circles. On the semi-circle ones, there's often an inner scale in the opposite direction of the outer one. Angles.

They are measured on a round scale in degrees, and one degree is one 360th of a turn.