Question

Proof the sum angle property of triangle​

Answer 1

$\huge \colorbox{blue}{ANSWER:-}$

To prove the above property of triangles, draw a line \overleftrightarrow {PQ} parallel to the side AC of the given triangle. Thus, the sum of the interior angles of a triangle is 180°.

Answer 2

Answer:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Proof:

Consider a ∆ABC. 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°.

Hope it is helpful to you.