first draw a ray .
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Well, honey, you start by drawing a line with your ruler. Then, you put the point of your compass on one end of the line and draw an arc. Next, you put the point of your compass on where the arc intersects the line and draw another arc. Where those arcs meet is your 32-degree angle. Voila!
with compass.........at 90+60degree angle,,,,,,,,, * * * * * and 90 + 60 = 105??? You need to draw a 90 degree ange and bisect it to give a 45 deg angle. Then add a 60 degree angle. 45 + 60 = 105.
In conjunction with a straight edge and a protractor
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.
The process can't reasonably be described with text only and no sketches. It consists of the following two major steps. They're both easy with a compass and a straight-edge: 1). Draw a straight line segment, then construct its perpendicular bisector. 2). Construct the angle bisector of any one of the four right angles formed in step-1.