why the sum of three sides of a triangle is 180 degree?
If your question is “Why the sum of three angles of a triangle is 180 degree?”, then the answer to this question is as given below.
Let us we are given a triangle PQR and ∠1, ∠2 and ∠3 are the angles of Δ PQR (figure shown below). We need to prove that ∠1 + ∠2 + ∠3 = 180°.
We use the properties related to parallel lines to prove this. For this, let us draw a line XPY parallel to QR through the opposite vertex P, as shown in the figure given below
Now, XPY is a line.
Therefore, ∠4 + ∠1 + ∠5 = 180° … (1)
But XPY || QR and PQ, PR are transversals.
So, ∠4 = ∠2 and ∠5 = ∠3 (Pairs of alternate angles)
Substituting ∠4 and ∠5 in (1), we get
∠2 + ∠1 + ∠3 = 180°
That is, ∠1 + ∠2 + ∠3 = 180°
because that's all the degrees that three sides of any length put together (a triangle) can hold- any less and it wouldnt even be a polygon, and any more and it would have to have more sides.
some more detail
A triangle has three angles. The angle sum property of a triangle defines that the sum of the three angles is always 180º
Let us see about the angle sum property of the triangle.
Here the base of the triangle has been extended and we get an exterior angle d which is adjacent to the interior angle c. As the sum of an interior angle and its adjacent exterior angle is 180º, c + d = 180º.
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Thus, We get c + d = 180º
c + a + b = 180º
a + b + c = 180º.
So the sum of three angles of a triangle is 180º. In any triangle ABC, the sum of the three triangles which can be given as
∠A + ∠B +∠C = 180º.