How can you divide an angle into 3 equal angles? You may only use a
straightedge and a compass to achieve this.
(This means : You have an angle A, you divide Angle A into 3 Angles B,C,D. And B=C=D=A/3)
Note: vohonam clarified that the problem actually only gives you a straightedge, not a ruler.
Since you have a ruler, not a straightedge, you can cheat. Draw an arc through the angle centered on the vertex. Measure the distance from the arc to the vertex and the distance between the two points at which the arc intersects the vertex. Divide the latter length by the former, then divide by two. You now have the sine of the angle. Calculate the arcsine. You now have the subtended angle.
Using the ruler, mark the halfway point between the two intersection points and draw a line through it. This is the angle bisector (you can also construct this using a compass and straightedge, but as long as we're cheating...). Take the angle you calculated earlier and divide by six. Calculate the sine of the new angle. Multiply this by the distance from the vertex to the intersection points. With your ruler connecting the two intersection points, measure this new distance out on either side of the angle bisector and mark those points. Draw lines through them. These last two lines will trisect the angle.
Solution, sorta.
