Question

Prove that the sum of the measures of three angles of a triangle is
180°​

Answer 1

Given :

Given :A triangle ABC.

Given :A triangle ABC.To prove :

Given :A triangle ABC.To prove :∠A+∠B+∠C=180

Given :A triangle ABC.To prove :∠A+∠B+∠C=180 o

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

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

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

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

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.

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 :

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,

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)

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)

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)

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

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]

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

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

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

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

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

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:

triangle PQR

$< 1 + < 2 + < 3 = 180$

= 180⁰