Definition of interior and exterior angles

In geometry, a triangle is a closed figure formed by three stopicIdes or three line segments. Triangle is the smallest polygon, it has three vertices, three stopicIdes & three angles in it. The triangle has three interior angles and six exterior angles. The angle instopicIde the triangle is known as interior angles. The angle outstopicIde the triangle is called an exterior angle.

The total interior and exterior angles differ. The total interior angles formed the angle sum property of a triangle. One of the most important properties of a triangle is applying the angle sum property of a triangle. 

Angle sum property of a triangle

There are three interior angles in a triangle and the sum of three interior angles is equal to 180°. It cannot be less than or more than 180°. 

In short, the angle sum property of a triangle says that the total interior angle of a triangle is always equal to 180°.

For example in triangle ABC, 

Measure angle A+ Measure angle B+ Measure angle C= 180°

Whether the triangle is obtuse angle triangle, acute angle triangle, right angle triangle, scalene triangle, Isosceles triangle, equilateral triangle, etc, the sum total of each triangle will equal 180. This will not be more than or less than 180°, the total will be exact 180°. This property is also used to calculate the unknown angles When the values of the other two angles are given.

Examples

For example, in a triangle PQR, angle P= 70° angle Q =40° find the value of measure angle R? 

Angle P + angle Q + angle R = 180°

70° +40° + angle R = 180°

110° + angle R = 180°

Angle R = 180° -110°

Angle R = 70°

Example: A triangle XYZ is an Isosceles triangle where angle Z= 60° and measure angle X and measure angle Y are the same. Find the measure of angles X and Y. 

Let Angle X = Angle Y= a ( as they are same) 

Angle X +Angle Y + Angle Z = 180°

a + a + 60° = 180°

2a + 60° = 180°

2a = 180° -60°

a= 120°/ 2

a= 60°

Angle X = Angle Y= 60°

Angle sum property formula

We can also find the sum of property by using a formula for any polygon. 

S= (n-2) * 180°

Where n= number of stopicIdes of polygon 

For example a triangle has three stopicIdes, n=3 

S= (n-2) * 180°

S= ( 3-2) * 180°

S= 1 * 180°

S= 180° Hence it is proved that by using this formula we can also find the angle sum property of a triangle or any polygon.

Features of angle sum property: 

The total interior angles of the triangle will always be equal to 180°. It will not be more than or less than 180°, it will be exactly 180°.

We can also use the angle sum property formula to find out the total of the triangle. 

            S= (n-2) * 180°

We can also use this formula or the property to find the unknown angle whenever the two stopicIdes of a triangle are given.