When two lines meet, at the point where they meet they are a distance apart. That distance will vary depending on how you measure it between the lines. But the ”wideness” of the space between the lines doesn’t change. The wideness is called the angle between the lines.

Now think of a circle and imagine two lines meeting at the centre of the circle. The wideness of the gap between the lines like a piece of pie can be related to the whole space surrounding the centre of the circle. So if we call this whole way round 360 degrees, like a pie cut into 360 pieces, we can measure the angle by counting how many pieces of pie there are between the lines. That’s the measure of the angle in degrees. A quarter of the pie would be 90 degrees and this is called a right angle. Any angle less than this is called acute. A straight line takes us half way round the circle (cut the pie in half) so the angle is 180 degrees. An angle between 90 and 180 is called obtuse and an angle bigger than 180 degrees is called reflex (because it is coming back on itself).

Why 360 degrees for the whole circle? Well, I guess it’s because the earth takes about 360 days to go round the sun, so each day is about one degree in the earth’s orbit, so it takes about 180 days (6 months) to get to the opposite side of the sun. At one time people may have thought a year was 360 days, and that idea has stuck and may explain why we use 360 degrees as the basic measure.