Question

prove that sum of the three angle of a triangle is 180°​

Answer 1

Answer:

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

.

hope it helps.....

Answer 2

Answer

To prove :-

Sum of all angles of a triangle is 180°

Construction :-

Through A,draw a line DAE || BC

Proof :-

→ DAE || BC and AB is the transversal.

→ ∠4 = ∠2 [ alternate interior angle ]

DAE || BC and AC is transversal.

→ ∠5 = ∠3 [ alternate interior angle ]

Now,DAE is a straight line.

→ ∠4 + ∠1 + ∠5 = 180° [ angles on the same side of DAE at point A ]

→ ∠1 + ∠4 + ∠5 = 180°

→ ∠1 + ∠2 + ∠3 = 180° [ °.°∠4 = ∠2 and ∠5 = ∠3]

Hence,sum of the angles of a triangle is 180°.

Note :- See the attachment for diagram.

_______________________________

Remarks :-

A triangle cannot have more than one right angle.

A triangle cannot have more than one obtuse angle.

In a right angle triangle,the sum of two acute angles is 90°.

hope  it will help you