Can you explain me the angle sum property of a triangle ?

Consider a triangle PQR in which ∠1, ∠2 and ∠3 are the angles of Δ PQR (figure shown below). Angle sum property of a triangle says that sum of the three angles in a triangle is 180 degrees, i.e.,

∠1 + ∠2 + ∠3 = 180^{0}.

We will now see the proof of the above statement.

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^{0} … (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^{0}

That is, ∠1 + ∠2 + ∠3 = 180^{0}

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