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Construct A 45 Degrees Angle

Related Topics: More Geometry Lessons


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.


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

In summary the steps to construct a 45° angle are:
1. Construct perpendicular lines to obtain a 90° angle.
2. Bisect the 90° angle to obtain a 45° angle.

How to construct a 45 degree angle using compass and straightedge?
Step 1: Construct perpendicular lines (90 degrees). Step 2: Bisect that angle to get a 45 degrees angle. How to construct a 30 degree angle without using a protractor?
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. How to construct a 75 degree angle with a compass?
Step 1: Construct 60 degree angles by constructing an equilateral triangle.
Step 2: Bisect a 60 degree angle to form a 30 degree angle.
Step 3: Bisect the 30 degree angle to form a 15 degree angle.
Step 4: Combine a 60 degree angle with a 15 degree angle to form a 75 degree angle.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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