Construct A 45 Degrees Angle

In this lesson, we will learn how to construct a 45 degrees angle by bisecting a 90 degrees angle.

We can use a similar angle bisector method 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.

Related Topics: More Geometry Lessons


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



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.

Bisection of an angle Construction 15, 30, 45, 60, 90, 135 degree angle

OML Search

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

OML Search