Question

proove that sum of all interior angles of a triangle is 180​

Answer 1

Answer:

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

o

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

o

Answer 2

Answer:

HEY BUDDY I HOPE IT HELPS YOU

Step-by-step explanation:

Q. Prove that the sum of all the interior angles of a triangle is 180°.

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 (adj. angles) --- eq(i)

And, ∠3 = ∠5 (adj. angles) --- eq(ii)

Now, Adding eq(i) and eq(ii)

Therefore, ∠2 + ∠3 = ∠4 + ∠5

∠1 + ∠2 + ∠3 = ∠1 + ∠4 + ∠5 [Adding ∠1 on both the sides]

∠1 + ∠2 + ∠3 = 180°

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

HEY BUDDY I HOPE IT HELPS YOU

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