Question

29) Prove that the sum of the 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

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given: AΔABC

To prove: ∠1+∠2+∠3=180°

Construction: through A, drawing a line XY||BC

Proof: Since 1||BC

Therefore,

∠2=∠4---------(1)

∠3=∠5--------(2)

Adding equation (1) and (2)

therefore,

∠2+∠3=∠4+∠5

Adding ∠1 both sides

∠1+∠2+∠3=∠1+∠4+∠5

∠1+∠2+∠3=180°

Thus,

The sum of three angles of a triangle is 180°