Question

prove angle sum
property of a triangle
​

Answer 1

To find the sum of interior angles of a polygon, we use this formula:-

(number of side of the polygon - 2) * 180

= (n-2)180

= (3-2)180

= 1*180

= 180

Hence, we proved the angle sum property for a triangle as sum of it's interior angles measure 180 degrees.

Answer 2

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.

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°