Question

prove that the sum of the angles of a triangle is 180°​

Answer 1

Answer:

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.

ZPAB + ZBAC + ZCAQ = 180°. where PQ line parallel to side BC touching vertex A.

ZAB = ZABC & CAQ = JCB BECAUSE alternate interior angles are congruent.

Hence we get, ZABC + ZBAC + ZACB = 180° [Proved]

Answer 2

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

.