Question

prove angle sum property of a triangle
STEP BY STEP EXAPLANATION

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.



 

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

∠PAB + ∠BAC + ∠QAC = 180°  ………(1)

SincePQ||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°.

Answer 2

Let a triangle ABC .
To prove -angle A + angle B +angle C = 180
Construction - Extend BC to D .
Proof - We know that , exterior angle of a triangle = sum of its opposite angles.
→ angle A + angle B = angle ACD....(1)
also , angle ACB+ angle ACD =180....(2)
Using (1) and (2), we get
angle A +angle B + angle C =180.