Question

prove that angle A,B,C are equal to 180°​

Answer 1

GIVEN :-

• ABC is a triangle.

TO PROVE :-

• Sum of angle of triangle is 180°.

CONSTRUCTION :-

• Draw a line DE || BC.

SOLUTION :-

In ∆ ABC,

→ DE || BC.

Therefore we can say that,

→ ∠5 = ∠1. ....Eq (1). [ alternate interior angles]

→ ∠4 = ∠2. ....Eq (2). [ alternate interior angles]

★ By linear pair theorem ★

→ ∠5 + ∠3 + ∠4 = 180°

Substitute ∠5 = ∠1 and ∠4 = ∠2.

→ ∠1 + ∠3 + ∠2 = 180°

→ ∠1 + ∠2 + ∠3 = 180°

Hence we prove that the sum of angle of triangle is 180°.

Hence proved ✅

Answer 2

To prove:-

∠A + ∠B + ∠C = 180° i.e = ∠1 + ∠2 + ∠3 = 180°

Construction:-

Through A, drawing a line L || to BC.

PROOF:-

Since L || BC Therefore,

∠2 = ∠4 [Alternate interior angles.]

∠3 = ∠5 [Alternate interior angles.]

Therefore,

= ∠2 + ∠3 = ∠4 + ∠5

= ∠1 + ∠2 + ∠3 = ∠1 + ∠4 + ∠5 [Adding ∠1 on both sides.]

= ∠1 + ∠2 + ∠3 = ∠4 + ∠1 + ∠5

= ∠1 + ∠2 + ∠3 = 180° [Since, sum of angles at a point on a line is 180° & ∠4 + ∠1 + ∠5 = 180°.]

Therefore,

∠A + ∠B + ∠C = 180°

Hence, proved.