Question

proof that sum of triangle of angle is 180​

Answer 1

Proof:

Consider a ∆ABC, as shown in the figure below. To prove the above property of triangles, draw a line PQ←→ parallel to the side BC of the given triangle.

Angle sum property of a triangle theorem 1

Since PQ is a straight line, it can be concluded that:

∠PAB + ∠BAC + ∠QAC = 180° ………(1)

Since PQ||BC and AB, AC are transversals,

Therefore, ∠QAC = ∠ACB (a pair of alternate angle)

Also, ∠PAB = ∠CBA (a pair of alternate angle)

Substituting the value of ∠QAC and∠PAB in equation (1),

∠ACB + ∠BAC + ∠CBA= 180°

Thus, the sum of the interior angles of a triangle is 180°.

Thankyou :)

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

o

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

o

.