Patterns of shapes using angles

To make patterns of shapes using different number of angles / types of angles

Let us recall the types of angles.

Observe the angles formed at the vertex of the following shapes.

This is an equilateral triangle.

It has 3 angles formed at 3 vertices.

The 3 angles are equal in measure and they are equal to 60°.

It can be demonstrated as follows.

Finding the angle of a regular hexagon using the equilateral triangle

We shall find the angles of a regular hexagon using the equilateral triangle. Place the equilateral triangles in a regular hexagon as shown in the figure.

Angle at the centre of a regular hexagon is 360°.

This is also the angle of a circle.

Angle at each vertex of a regular hexagon is 120°

Finding the angle of a square

Angle of a circle is 360° 

Let us find the angle of square using a circle.

Place 4 squares as shown in the above figure.

The shape formed at the centre is a circle. The angle of circle is 360°.

Now the angle of a square is 360° ÷ 4 = 90°.