How do you draw angle 112.5 using ruler and compass?

Answer 1

You need to know how to bisect an angle:

1. Open your compasses to some (shortish) length;
2. with the point of the compasses on the point of the angle draw an arc on each arm of the angle;
3. extend the compasses to a longer length.
4. with the point of the compasses on each point where the arcs intersect the arms, draw two further arcs (away from the point of the angle) between the arms of the angle so that they cross;
5. using the rule draw a straight line from the point of the angle to the point where the last two arcs drawn cross.

Now to create your 112.5o angle:

1. Draw a straight line and mark a point near the middle. This is the point of your angle; call it O
2. Bisect the 180o angle at O (one side of the straight line), creating two 90o angles. (This is usually called creating the perpendicular to the line at point O.)
3. Bisect one of the 90o angles, creating two 45o angles.
4. On the opposite side to the angle bisected in step 2 is another 180o angle; to this add the 45o angle next to the original straight line. This creates a 225o angle.
5. Bisect the angle found in step 4, creating the required 112.5o angle.

After step 4 you should have something like this:

. . . . . . . . . . . .B

. . . . . . | . . . . / .

. . . . . . | . . . / . .

. . . . . . | . . / . . .

. . . . . . | . / . . . .

. . . . . . | / . . . . .

A------+--------

. . . . . .O . . . . . .

reflex angle ∠AOB is the 225o angle to bisect in step 5 to create your 112.5o angle.