An infinite number.
It is relatively simple to draw a perpendicular bisector and so you have a 90 degree angle. It is also simple to bisect an angle and so you can make a 45 deg angle and, if you add it to the other side of the 90 deg, a 135 deg angle. Bisect these and you can make 22.5 deg, 67.5 deg, 112.5 deg and 157.5 deg.
You can keep bisecting angles and adding them to either side of the angles that you have already got. In theory, there is no limit to the number of times this process can be repeated - except the lifespan of the universe.
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A compass
To construct an angle of 150 degrees using a compass, you would first draw a ray as the initial side of the angle. Then, place the compass on the vertex of the angle and draw an arc that intersects the initial ray at a point. Next, without changing the compass width, place the compass on the intersection point and draw another arc that intersects the previous arc. Finally, draw a ray from the vertex through the point of intersection of the two arcs to create an angle of 150 degrees.
two supplementary angles * * * * * NO! Supplementary angles sum to 180 degrees = 2 right angles. The correct answer is complementary angles.
In math a compass is an object used to draw accurate circles and arcs (parts of circles, or curves). In math, a compass is something that makes a circle and it also measures circumference. How to make a circle: A compass either has led in it or you stick a pencil in it, but it depends on what kind of compass it is. If you want to make a big circle, you expand the 2 sides. when you get it to the size you want, you stick it on paper and twirl it around. It may not be a perfect circle but it most likely will be close.