Question

To prove that the sum of the three angles if triangles is 180°.​

Answer 1

Given :

A triangle ABC.

To prove :

∠A+∠B+∠C=180

o

⟹∠1+∠2+∠3=180

o

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 = 0

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Answer 2

$\huge\bf\boxed{\boxed{\underline{\red{Question!!}}}}$

To prove that the sum of the three angles if triangles is 180°.

$\huge\bf\boxed{\boxed{\underline{\red{Answer!!}}}}$

$\huge\bold{Given}$

That the sum of the three angles if triangles is 180°.

Let the triangle Be ∆PQR

$\huge\bold{To \:prove}$

$\huge\mathrm\red{∠1 \:+ \:∠2 \:+ \:∠3 = 180°}$

Let's do the construction :

Draw the line AB passes thought P and parallel to QR

$\huge\bold{Proof}$

A line AB || QR with transversal of PQ

➪ ∠2 = ∠4 [ Alternate angle ] ----------(1)

A line AB ||QR with transversal of PR

➪ ∠3 = ∠5 [ Alternate angle ] ----------(2)

So the line AB

☞︎︎︎ ∠1 + ∠4 + ∠5 = 180° [ Linear pair ]

☞︎︎︎ ∠1 + ∠2 + ∠3 = 180° ( from eq (1) and (2) )

$\huge\bold{Hence \:proved}$

$\huge\bold{refer \:the \:attachment \:for \:the \:daigram}$