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Construct A 45 Degrees Angle

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

We can use the 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.

construct 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.
Constructing a 30 degree angle
This video shows two ways to construct a 30 degree angle. The first way starts by constructing part of an equilateral triangle, then bisecting the 60 degree angle. The second method starts by constructing a rhombus with 60 and 120 degree angles, then joining the opposite vertices to leave the 30 degree angle.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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