Question

Prove that, Sum of measures of angles of triangle are 180°.
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Answer 1

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∥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

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

Answer 2

Answer:

By EULER'S formula,

where "n" = no. of sides.

No. of sides in a triangle = 3.

So, measure of all angles of a triangle = (3-2)×180° = 1×180° = 180°. I HOPE IT HELP YOU.