how to construct an angle of 67.5 degrees and 45.5 degrees with a compass and ruler

A 45˚ angle can be obtained by bisecting a 90˚ angle.

Construct a 90˚ angle, and then construct an angle bisector to obtain a 45˚ angle.

**Step 1** : Stretch your compasses until it is more then half the length of *AB*. Put the sharp end at *A* and mark an arc above and another arc below line segment *AB*.

**Step 2** : Without changing the width of the compasses, put the sharp end at *B* and mark arcs above and below the line segment *AB* that will intersect with the arcs drawn in step 1.

**Step 3** : Join the two points where the arcs intersect with a straight line. This line is the perpendicular bisector of *AB*. *P *is the midpoint of* AB*.

Step 4: Bisect the 90 degree angle to form a 45 degree angle.

After getting this we have two 45 degree angles, bisect any 1 of these angles yoy will get two 22.5 degree angles

**So add the 45 degree with the 22.5 degree, you will get a 67.5 degree angle**

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