Understanding an Exterior Angle 

In geometry, we all know about triangles. It is a form of a polygon. Angles created between two polygons' stopicIdes and their extended neighboring stopicIdes are known as exterior angles. In order to find out the exterior angle, the sum of two stopicIdes of the interior angle is always equal to its exterior angle. 

We can also use this to find the measure of the unknown angle of a triangle. The sum of the measure of exterior angles of a triangle is 360°.

A triangle's exterior angle measurement is equivalent to the total of the interior angle measurements of the two non-adjacent stopicIdes. It means an exterior angle is equal to the addition of the two angles not right next to it.

Example : 

 To find the exterior angle PRS, we use formula 

Sum of two opposite interior angles = exterior angles 

Angle Q +  Angle P= Angle PRS 

45° +65°= 110°

Therefore angle PRS = 110°

Exterior angle theorem formula 

As for the exterior angle property theorem of the triangle

The combination of two interior angles is equivalent to the outstopicIde angle's measure.

Please note that an exterior angle is supplementary to the adjacent interior angles as they form the linear pair of angles. This theorem can be used to find the measure of an unknown angle given in a triangle. 

Important features

⦁ The sum of the measure of the exterior angles of any triangle is always 360°. 

⦁ Exterior angle inequality states that a triangle's exterior angle is always bigger than either of its internal opposed angles.

⦁ The exterior angle and the next interior angle together form a linear pair of 180 degrees. The exterior angle and the adjacent interior angles are supplementary that is 180°.

⦁ The angle sum property of a triangle of interior angles mentions that the sum of all interior angles is 180 degrees.

⦁ There are six exterior angles in a triangle so the measure of all six exterior angles is 360°

Example 

 In the given figure, triangle ABC

Angle B= 90 degree  

Angle A = 30 degree

Angle ACD =? ( exterior angle) 

As the theorem, the addition of any two interior angles, opposite to each other, is equivalent to an exterior angle 

Angle B + Angle A= Angle ACD

90° + 30°= Angle ACD

Angle ACD= 120°

As you know when all the exterior angles of a polygon are added, you get 360°. The technique of finding out the magnitude of an exterior angle is in the following way: 

You shall find an exterior angle when you divtopicIde 360° by the number of existing stopicIdes of the polygon (360 degree/ no. of stopicIdes will give you exterior angle).

For example: 

A triangle has three stopicIdes.  Suppose you want to find all exterior angles’ sizes.

An exterior angle of a polygon= 360° divtopicIded by the number of stopicIdes

                                           = 360° / 3 

                                           = 120° 

Each size of the exterior angle of a triangle is 120°.