Question

Show that the sum of the angles of a triangle is 180°​

Answer 1

Answer:

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

Answer:

Given :  A triangle ABC.

To prove :  ∠A+∠B+∠C=180

⟹∠1+∠2+∠3=180  

Construction :  Through A, draw a line l parallel to BC.

Proof :

Since l II BC. Therefore,

∠2=∠4________________________(i)

And, ∠3=∠5_____________________(ii)

adding  eq(i) and (ii)

Therefore, ∠2+∠3=∠4+∠5

∠1+∠2+∠3=∠1+∠4+∠5  [adding∠1bothSide]

∠1+∠2+∠3=180  

Thus, the sum of three angles of a triangle is 180

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