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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 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

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.


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.



 

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