Question

prove that the sum of all interior angles of a tringles is 180°.​

Answer 1

Answer:

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

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

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Answer 2

Step-by-step explanation:

Given ABC is a triangle

To prove : <1+<2+<3=180°

Construction: Through A draw a line DE parallel to BC.

Proof: DE||BC and AB is transversal

Therefore,<1=<4.............(1) [alternate interior angles]

DE||BC and AC is transversal .,

Therefore,<2=<5...........(2) [alternate interior angles]

Therefore,<1+<2=<4+<5

[ adding corresponding sides of (1) and (2)]

so,. <1+<2+<3=<4+<5+<3 [ adding <3 to both sides ]

But <4+<5+<3=180

[<DAE is a straight angle]

Therefore,<1+<2+<3=180°

hence the sum of angles of a triangle is 180°..

hope helps you!