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More Geometry Lessons

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

**How to construct a 45° angle by bisecting a 90° angle?**

**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.

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.

More Geometry Lessons

In this lesson, 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 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.

**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.

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.

Step 1: Construct perpendicular lines (90 degrees). Step 2: Bisect that angle to get a 45 degrees 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.

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.

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