You use a protractor
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Yes by bisecting an angle of 140 degrees with a compass
It is easy to draw an equilateral triangle without a protractor. That gives a 60 degree angle. It is then simply a matter of bisecting the 60 degree angle, using an unmarked rule and compass, to get a 30 degree angle.
To construct a 54-degree angle with a compass, start by drawing a straight line using a ruler. Place the compass on one endpoint of the line and draw an arc that intersects the line. Without changing the compass width, place the compass on the intersection point and draw another arc. Where the two arcs intersect is a point that, when connected to the endpoint of the line, forms a 54-degree angle.
By bisecting an angle of 30 degrees using a compass and a straight edge
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.