Question

Prove that the sum of angle of a triangle is always 180

Answer 1

Step-by-step explanation:

Let's add some angle labels to all the angles between the parallel lines: We can see that angles A, B, and C combine to form a straight angle, so that means that their sum must be 180 degrees. Now we can establish that the three angles inside the triangle (B, E & F) also add up to 180.

Answer 2

Answer:

Given :

A triangle ABC.

To prove :

∠A+∠B+∠C=180degrees

⟹∠1+∠2+∠3=180degrees

 

Construction :

Through A, draw a line l parallel to BC.

Proof :

Since l∥BC. Therefore,

∠2=∠4 __________equation(i)

And, ∠3=∠5________equation(ii)

adding  equation (i) and (ii)

Therefore, ∠2+∠3=∠4+∠5

∠1+∠2+∠3=∠1+∠4+∠5  [adding∠1 both Side]

∠1+∠2+∠3= 180 degrees

 

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

           (or) we can prove like this ↓↓↓

• In order to prove that the sum of angles of a triangle is 180, you must know the theorems of angles of a triangle.

• We know that,  alternate interior angles are of equal magnitude.

• This'll help us get the answer. Let us assume a triangle ABC. Now we have to substitute the angles.

∠PAB + ∠BAC + ∠CAQ = 180°. where PQ line parallel to side BC touching vertex A.

∠PAB = ∠ABC & ∠CAQ = ∠ACB BECAUSE alternate interior angles are congruent..

Hence we get, ∠ABC + ∠BAC + ∠ACB = 180°   [Proved]