# Interior and exterior angles in triangle

From Karnataka Open Educational Resources

Angles are formed when three lines intersect with each other. There are angles that are enclosed by the three lines and there are angles that are formed outside the closed figure.

## Contents

### Objectives

- Identify all angles when a triangle is formed
- Understand the relation between various angles that are formed in a triangle.

### Estimated Time

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

Prior knowledge of point, lines, angles

### Materials/ Resources needed

- Digital : Computer, geogebra application, projector.
- Non digital : Worksheet and pencil.
- Geogebra files :
**“Angles of triangle.ggb”**

Download this geogebra file from this link.

### Process (How to do the activity)

- Ask students how many lines are there? They should be able to identify the points of intersection of the lines. How many points of intersection are formed?
- How many angles are formed at an intersecting point? How many angles in total at the three points of intersection?What is the total angle measure at each intersecting point?
- How many angles are inside the triangle and how many are outside the triangle
- Can you find an exterior angle that is equal to the interior angle of a triangle at each vertex?Why are they equal?
- Identify the exterior angles that are equal? Justify why they are equal.
- Establish that there are 2 angles which are exterior of the triangle that are equal and are formed when the sides of the triangle is extended at the vertex.
- Students to analyze the interior and exterior angle at each point to find a relation between the interior angle and one of the exterior angles at the vertex. Students should be able to recognize the linear pair formed by interior angle and exterior angle.
- Vary the position of the lines to check if interior and exterior angles form a linear pair.

- Note the measure of angles

Angles of the triangle | Exterior angle | Interior angle + Exterior angle | ||||||
---|---|---|---|---|---|---|---|---|

Angle 1 | Angle 2 | Angle 3 | Angle 1 | Angle 2 | Angle 3 | In Angle 1 +
Ex Angle1 |
In Angle 2 +
Ex Angle2 |
In Angle 3 +
Ex Angle3 |

. | ||||||||

. |

**Evaluation at the end of the activity**

- Are students able to recognize interior and exterior angles in a triangle
- Have the students able to find a relation between the interior angle and exterior angle that are formed at each vertex?