Constructing a 45° angle

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See also the animated version.

After doing this Your work should look like this
1.  Draw a line segment which will become one side of the angle. (Skip this step if you are given this line.) The exact length is not important. Label it PQ. P will be the angle's vertex. Geometry construction with compass and straightedge or ruler or ruler
In the next 3 steps we create the perpendicular bisector of PQ.
See Constructing a perpendicular bisector of a line segment
2.  Set the compasses' width to just over half the length of the line segment PQ. Geometry construction with compass and straightedge or ruler or ruler
3.  With the compasses' point on P then Q, draw two arcs that cross above and below the line. Geometry construction with compass and straightedge or ruler or ruler
4.  Draw a line between the two arc intersections. This is at right angles to PQ and bisects it (divides it in exactly half). Geometry construction with compass and straightedge or ruler or ruler
 
5.  With the compasses' point on the intersection of PQ and the perpendicular just drawn, set the compasses' width to P Geometry construction with compass and straightedge or ruler or ruler
6.  Draw an arc across the perpendicular, creating the point C Geometry construction with compass and straightedge or ruler or ruler
7.  Draw a line from P through C, and on a little more. The end of this line is point R Geometry construction with compass and straightedge or ruler or ruler
8.  Done. The angle QPR has a measure of 45° Geometry construction with compass and straightedge or ruler or ruler

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