Question

show that s of exterior angle in a triangle is 360°

Answer 1

An exterior angle of a triangle is equal to thesum of the opposite interior angles. For more on this seeTriangle external angle theorem. If the equivalentangle is taken at each vertex, the exterior angles always add to 360° In fact, this is true for any convex polygon, not just triangles.

Answer 2

We know that sum of angles in a triangle is 180°

i.e in ΔABC,

∠A + ∠B + ∠C = 180°

The exterior angles of ΔABC are 180° - ∠A, 180° - ∠B and 180° - ∠C

Sum of exterior angles = 180° - ∠A + 180° - ∠B + 180° - ∠C

                                     = 180° + 180° + 180° - (∠A + ∠B + ∠C)

                                    = 360° + 180° - 180°

                                    = 360°