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