Construct A 45 Degree Angle

We can use the angle bisector to construct some other angles from existing angles.

Example :

A 30˚ angle can be obtained by bisecting a 60˚ angle.
A 15˚ angle can be obtained by bisecting a 30˚ angle.
A 45˚ angle can be obtained by bisecting a 90˚ angle.
A 22.5˚ angle can be obtained by bisecting a 45˚ angle.

Example:

The figure shows a point A on a straight line. Construct an angle of 45˚ at point A.

Solution:

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.

The following video shows how to construct a 45 degree angle using compass and straightedge. First, construct perpendicular lines (90 degrees) and then bisect that angle to get a 45 degrees angle.

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