# Constructing different angles and shapes

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In this lesson, we will look at constructing different angles and shapes using a compass and a straight edge.

• A 90° angle can be obtained by constructing a perpendicular bisector.
• A 45° angle can be obtained by bisecting a 90° angle.
• A 22.5° angle can be obtained by bisecting a 45° angle.
• A 60° angle can be obtained by constructing an equilateral triangle.
• A 30° angle can be obtained by bisecting a 60° angle.
• A 15° angle can be obtained by bisecting a 30° 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.

The following video shows

• how to bisect a line
• how to bisect an angle
• how to construct a right angle
• how to construct a 60° angle
• how to construct a hexagon

The following video shows

• how to construct a 120° angle
• how to construct a 45° angle
• how to construct a 30° angle
• how to construct an equilateral triangle
• how to construct triangle given 3 sides using compasses

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