Question

Q.1 Prove that sum of the angles of triangle is 180°​

Answer 1

Given :

A triangle ABC.

To prove :

∠A+∠B+∠C=180

∠1+∠2+∠3=180

Throughout A, draw a line l parallel to BC.

Answer 2

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$\sf\colorbox{cyan}{✰ Given }$

A triangle ABC

$\sf\colorbox{cyan}{✰ To prove}$

A+∠B+∠C=180°

⟹ ∠1 + ∠2 +∠3 = 180°

$\sf\colorbox{cyan}{✰ Construction }$

Through A , draw a line l parallel to BC.

$\sf\colorbox{cyan}{✰ Proof }$

Since ( 1 ) || BC. Therefore,

∠2 = ∠4 $\tt\red{[ ☦ equation - (1) ☦ ]}$

And , ∠3 = ∠5 $\tt\red{[ ☦ equation - (2) ]}$

adding eq(1) and (2)

Therefore, ∠2 + ∠3 = ∠4 + ∠5

∠1 + ∠2 + ∠3 = ∠1 + ∠4 + ∠5

[ adding ∠1 both Side ]

∠1 + ∠2 + ∠3 = 180°

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

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