Question

why the sum of angles in triangle is 180 why not 360 or 240

Answer 1

Answer:

A triangle's angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle.

Answer 2

Answer:

Step-by-step explanation:

Let's prove this step by step:

Given : A triangle, ΔABC

To prove: Sum of all angles of the triangle is 180

                ∠ABC + ∠BAC + ∠BCA = 180°

Construction: draw a line passing through point A which is                                             parallel to BC.

Proof:

By the property of alternate angles, we can say that

           ∠XAB = ∠ABC            -----------1

           and ∠YAC = ∠ACB     -----------2

Now by straight line property that sum of angles made                by three points lying on the same straight line is 180°.

∠XAB + ∠BAC + ∠YAC = 180°

Using equation 1 and 2

∠ABC + ∠BAC + ∠BCA = 180°

Hence proved