Question

I WANT THE PROOF OF ANGLE SUM PROPERTY.

ANSWER WILL BE MARKED AS BRAINLIEST

Answer 1

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.

Figure 2 Proof of angle sum property

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

∠PAB + ∠BAC + ∠QAC = 180°  ………(1)

SincePQ||BCand AB, AC are the transversals,

Therefore, ∠QAC = ∠ACB (pair of alternate angles)

Also, ∠PAB = ∠CBA(pair of alternate angles)

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

∠ACB + ∠BAC + ∠CBA= 180°

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