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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

*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 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.

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.