# why the sum of three sides of a triangle is 180 degree?

Hi Devisha!

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°

Cheers!

• 0

you are wrong.sum of three angles is 180 degrees

• -2
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 Proof:

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.

• 3

thankssssss

• 0
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