Question

theoretically prove that the sum of interior angles of a triangle is 180
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Answer 1

Step-by-step explanation:

To prove the above property of triangles, draw a line \overleftrightarrow {PQ} parallel to the side BC of the given triangle. Thus, the sum of the interior angles of a triangle is 180°.

Answer 2

Hi!

Here is the answer to your query.

Consider a triangle PQR and ∠1, ∠2 and ∠3 are the angles of ΔPQR (figure shown below). We need to prove that ∠1 + ∠2 + ∠3 = 180°.

XPY is a line.

∴∠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°

∴∠1 + ∠2 + ∠3 = 180°

Cheers!