# Relation between interior and exterior angles in triangle

From Karnataka Open Educational Resources

Interior angle and the corresponding angle form a linear pair. This exterior angle in relation to the remote interior angles and their dependencies are deducted with the theorem.

## Contents

### Objectives

To show interior angles of a triangle have a relation with its exterior angles.

### Estimated Time

40 minutes

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

Prior understanding of point, lines and angles, adjacent angles, vertically opposite angles, linear pair

### Materials/ Resources needed

- Digital : Computer, geogebra application, projector.
- Non digital : Worksheet and pencil.
- Geogebra files :

Download this geogebra file from this link.

Download this geogebra file from this link.

Download this geogebra file from this link.

### Process (How to do the activity)

- In the triangle students should identify the angles of the triangle.
- Extend one side, students should recognize the exterior angle formed.
- What is the sum of the angles of a triangle?
- Students should be able to recognize the alternate angle formed for one of the interior angle(Angle BAC)
- Drag the parallel line to the opposite vertex, to place the alternate angle next to the angle at the opposite vertex.
- Compare the angles formed and the exterior angle, do they have a relation.
- How are the two angles together related to the exterior angle?
- Do you notice any relation between the exterior angle and the interior angles
- If you know the measure of interior angle can you find the corresponding exterior angle?
- The other two files can be used to demonstrate the the relation between the exterior angle and opposite interior angles.
- Note the measure of angles

Triangle | Angle A | Angle B | Angle C | Exterior angle | Angle A + Angle B |
---|---|---|---|---|---|

Triangle1 | |||||

Triangle2 | |||||

Triangle3 |

**Evaluation at the end of the activity**

- Have the students able to identify the relation between exterior and interior opposite angles of a triangle?