Question

show that the sum of angle of a triangle is 180°​

Answer 1

$\large{ \underline{ \underline{ \red{Solution}}}}$

Given:

A triangle ABC,

To prove:

∠A + ∠B + ∠C = 180° => ∠1 + ∠2 + ∠3 = 180°

Construction:

Through A, draw a line l parallel to BC.

Proof:

Since 1 || BC. Therefore,

∠2 = ∠4__eq......(i)

And,

∠3 = ∠5__eq.......(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°

Since, the sum of the angle of a triangle is 180°.