How do you construct 80 degree angle using compass and ruler?

Draw a point, and a long straight line through it. Put the centre of the compass over the point, with north on the compass (or zero degrees) on the line. Then draw a second line out from the point at 80 degrees on the compass. You'll then have a 80 degree angle between the lines.

It's usually a trick that teachers decide to do on their pupils. A compass is what you use to find north and a pair of compasses is used to draw circles.