Question

Prove that sum of interior angles in a triangle is 180°

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Answer 1

Answer:

Let us use the formula:-

(N - 2) × 180

Where N is number of sides

Let us solve:-

$\sf(3 - 2) \times 180$

$\sf \to(3 - 2) \times 180$

$\sf \to1 \times 180$

$\sf \to180 \degree$

Answer 2

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∥BC. Therefore,

∠2=∠4 ..............eq(i)

And, ∠3=∠5.............eq.(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°