Angles of Triangle

There are three angles in a triangle. These angles are formed by two sides of the triangle, which meets at a common point, known as the vertex. The sum of all three interior angles is equal to 180 degrees. 

If we extend the side length outwards, then it forms an exterior angle. The sum of consecutive interior and exterior angles of a triangle is supplementary. 

Let us say, ∠1, ∠2 and ∠3 are the interior angles of a triangle. When we extend the sides of the triangle in the outward direction, then the three exterior angles formed are ∠4, ∠5 and ∠6, which are consecutive to ∠1, ∠2 and ∠3, respectively.

Hence, 

∠1 + ∠4 = 180°   ……(i)

∠2 + ∠5 = 180°  …..(ii)

∠3 + ∠6 = 180°  …..(iii)

If we add the above three equations, we get;

∠1+∠2+∠3+∠4+∠5+∠6 = 180° + 180° + 180°

Now, by angle sum property we know, 

∠1+∠2+∠3 = 180°

Therefore, 

180 + ∠4+∠5+∠6 = 180° + 180° + 180°

∠4+∠5+∠6 = 360°

This proves that the sum of the exterior angles of a triangle is equal to 360 degrees.

Properties

Each and every shape in Maths has some properties which distinguish them from each other. Let us discuss here some of the properties of triangles.

1. A triangle has three sides and three angles.
2. The sum of the angles of a triangle is always 180 degrees.
3. The exterior angles of a triangle always add up to 360 degrees.
4. The sum of consecutive interior and exterior angle is supplementary.
5. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Similarly, the difference between the lengths of any two sides of a triangle is less than the length of the third side.
6. The shortest side is always opposite the smallest interior angle. Similarly, the longest side is always opposite the largest interior angle.