Lines and Angles

Look around you: scissors, clock hands, a book opening. All of them make angles, and today we learn to measure them. Let's start with a line. It goes on forever in both directions, so we draw little arrows at both ends. A ray starts at one point and goes on forever in one direction. A line segment has two ends and is a fixed length.

Now take two rays that start from the same point. They open up like a pair of scissors, and that opening is an angle. The shared starting point is called the vertex. Here it is the centre of the circle. The two rays are the arms of the angle. One lies flat, and the other has turned.

The size of an angle tells us how much one arm has turned. We measure it in degrees.

Turn the arm a little more, to ninety degrees. This is a right angle, like the corner of your book.

Any angle smaller than ninety degrees is called an acute angle. It is a sharp, small opening.

An angle bigger than ninety but smaller than one eighty is an obtuse angle. It is wide open.

At one hundred eighty degrees, the arms point in opposite directions and make a straight line. This is a straight angle.

Keep turning until the arm comes all the way back to the start. That full turn is three sixty degrees.

Here is a neat idea. A right angle is a quarter turn, so a half turn is two right angles. Let's work one out. A quarter turn is ninety degrees, so a half turn is ninety plus ninety.

Ninety plus ninety gives one hundred eighty degrees, which matches the straight angle we saw.

Two lines that meet to make a right angle are called perpendicular lines. Think of the corner of a window. A common mistake is thinking a bigger drawing means a bigger angle. Angle size depends on the opening, not the length of the arms. In real life, look at a clock. At three o'clock, the hands make a perfect right angle.

At six o'clock, the hands point opposite ways and make a straight angle of one hundred eighty degrees. Now try this quiz with a new angle. An angle of one hundred ten degrees is which type? To sum up: an angle is two arms meeting at a vertex, measured in degrees, from acute to right, obtuse, straight and a full turn.