# Sum of the interior angles of a quadrilateral

From Karnataka Open Educational Resources

The sum of the measures of the angles in any quadrilateral is 4 right angles.

### Objectives

To establish that sum of interior angles of any quadrilateral is 360°

### Estimated Time

40 minutes

### Prerequisites/Instructions, prior preparations, if any

Prior knowledge of point, lines, angles, intersecting lines, vertically opposite angles, properties of triangle

### Materials/ Resources needed

- Digital: Computer, geogebra application, projector.
- Non digital : Worksheet and pencil
- Geogebra files : ‘Sum of the interior angles of a quadrilateral.ggb’

Download this geogebra file from this link.

### Process (How to do the activity)

- In the geogebra sketch for the quadrilateral measure the sides and angles at the vertices
- Calculate the sum of these angles of the quadrilateral? Note your observations

Quadrilateral | Side1 | Side2 | Side3 | Side4 | Angle1 | Angle2 | Angle3 | Angle4 | Angle1+Angle 2+ Angle3 + Angle 4 | Whatdo you observe about their sum |

Q1 | ||||||||||

Q2 | ||||||||||

Q3 |

- Draw any one diagonal. What do you notice? What is the quadrilateral divided into? How many triangles are formed?
- What is the measure of the sum of angles in each quadrilateral? So what is the measure of all the angles of the quadrilateral?
- Make different quadrilaterals. Divide it into two triangles, measure the angles of the two triangles, check their sum.
- Tabulate the angles of the two triangles

Observation | Triangle1 | Triangle2 | Sum of angles of two triangle | ||||||

Angle 1 | Angle 2 |
Angle 3 |
Sum of angles | Angle 1 | Angle 2 |
Angle 3 |
Sum of angles | ||

Q1 | |||||||||

Q2 | |||||||||

Q3 |

**Evaluation at the end of the activity**

- Is the sum of all angles in any quadrilateral 360
^{o}.