Question

prove the sum of angle of triangle is 180°​

Answer 1

Step-by-step

Given :

Given :A triangle ABC.

Given :A triangle ABC.To prove :

Given :A triangle ABC.To prove :∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180o

Given :A triangle ABC.To prove :∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180oConstruction :

Given :A triangle ABC.To prove :∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180oConstruction :Through A, draw a line l parallel to BC.

Given :A triangle ABC.To prove :∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180oConstruction :Through A, draw a line l parallel to BC.Proof :

Given :A triangle ABC.To prove :∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180oConstruction :Through A, draw a line l parallel to BC.Proof :Since l∥BC. Therefore,

Given :A triangle ABC.To prove :∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180oConstruction :Through A, draw a line l parallel to BC.Proof :Since l∥BC. Therefore,∠2=∠4 .......eq(i)

Given :A triangle ABC.To prove :∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180oConstruction :Through A, draw a line l parallel to BC.Proof :Since l∥BC. Therefore,∠2=∠4 .......eq(i)And, ∠3=∠5......eq(ii)

Given :A triangle ABC.To prove :∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180oConstruction :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)

Given :A triangle ABC.To prove :∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180oConstruction :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

Given :A triangle ABC.To prove :∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180oConstruction :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]

Given :A triangle ABC.To prove :∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180oConstruction :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=180o

Given :A triangle ABC.To prove :∠A+∠B+∠C=180o⟹∠1+∠2+∠3=180oConstruction :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=180oThus, the sum of three angles of a triangle is 180o.

Answer 2

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 degree

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