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How to find a measure in each angle?
by using a ruler
How do you make an angle of 150 degree with 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.
Which constructions is impossible using only a compass and straightedge?
doubling the cube
How many angles can we make using ruler and compass?
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.
How you would construct a regular hexagon using a compass?
First draw a circle. Keeping the compass at the same angle; from any point on the circle's edge, draw another arc that intersects the circle's edge and (should) go through the centre as well. Repeat these arcs until you get back to the start. Using a ruler, connect the six intersect points on the edge of the circle and erase the construction lines.
