Question

Prove that sum of exterior angles formed by succeeding sides of triangles is 360 degree​

Answer 1

Given:

• In ΔABC, Sides BC, produced

To prove :

• ∠1+ ∠2 + ∠3 = 360°.

Proof:

∠1 = ∠5+ ∠6

[By exterior angle property].(1)

∠2 = ∠4 + ∠6

[By exterior angle property].(2)

∠3 = ∠4 + ∠5

[By exterior angle property](3)

On adding equation (1), (2) and (3) we get

∠1 + ∠2 + ∠3 = 2 x [∠4 + ∠5 + ∠6]

∠1 + ∠2 + ∠3 = 2 x 180°

[ ∠4 + ∠5+ ∠6= 180° by ASP of Δ ]

∠1 + ∠2 + ∠3 = 360° Ience Proved.

Answer 2

Question:-

Prove that sum of exterior angles formed by succeeding sides of triangles is 360 degree.

To Find:-

We have to prove that exterior angles formed by succeeding sides of triangles is 360°.

Solution:-

exterior angles :- x , y , z

Prove :- x + y + z = 360°

Sum of the interior angles ∠s of triangle TS always 180°.

linear pair is 180°

∠A + ∠B + ∠C = 180°

x = 180° - ∠B

y = 180° - ∠C

z = 180° - ∠A

➭ x + y + z = 3(180°) - ∠A - ∠B - ∠C

➭ x + y + z = 3(180°) - (∠A +∠B +∠C)

➭ x + y + z = 3(180°) - 180°

➭ x + y + z = 180°( 3 - 1 )

➭ x + y + z = 180° (2)

➭ x + y + z = 360°

☞ Hence Proved