5th Maths Unit 3: Patterns of Shapes Using Angles - Term 2 Study Guide

Patterns | Term 2 Chapter 3 | 5th Maths - Patterns of shapes using angles | 5th Maths : Term 2 Unit 3 : Patterns

Chapter: 5th Maths : Term 2 Unit 3 : Patterns

Patterns of shapes using angles

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

Let us recall the types of angles.

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 \(60^\circ\).

It can be demonstrated as follows.

Equilateral Triangle demonstration
Finding the angle of a regular hexagon using the equilateral triangle
Regular Hexagon and 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.

Hexagon pattern formation

Angle at the centre of a regular hexagon is \(360^\circ\).

This is also the angle of a circle.

Angle at each vertex of a regular hexagon is \(120^\circ\)

Hexagon angle calculation
Finding the angle of a square

Angle of a circle is \(360^\circ\) Circle Icon

Let us find the angle of square using a circle.

Square pattern from circle

Place 4 squares as shown in the above figure.

The shape formed at the centre is a circle. The angle of circle is \(360^\circ\).

Now the angle of a square is \(360^\circ \div 4 = 90^\circ\).

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