Question

Bonjour Brainliacs!

Prove that The sum of 3 exterior angles of a triangle = 360°

Answer 1

Bonjour Darlo!!

Your answer :-

↪ We all are familiar with the Angle Sum Property => Angle ABC + Angle BCA + Angle CAB ( Refer to the attachment ) = 180°


↪ Angle 1 + Angle 2 = 180° ( Linear Pair )

↪ Angle 3 + Angle 4 = 180° ( Linear Pair )

↪ Angle 5 + Angle 6 = 180° ( Linear Pair )

Now adding all the angles!

↪ Angle ( 1 + 2 + 3 + 4 + 5 + 6 ) = 180° + 180° + 180°

↪ Sum of all angles = 540°

↪ Sum of all interior angles = 180° ( A.S.P. )

↪ Subtracting

↪ Sum of all angles - Sum of all interior angles = Sum of all exterior angles

↪ 540° - 180° = Sum of all exterior angles

↪ 360° = Sum of all exterior angles

Hence, Proved #

☆ Hope it helps ☆

Answer 2

Question-

Prove that the sum of the exterior angles of a triangle is equal to 360 degrees.

Answer-

Let us say, ∠1, ∠2 and ∠3 are the interior angles of a triangle. When we extend the sides of the triangle in the outward direction, then the three exterior angles formed are ∠4, ∠5 and ∠6, which are consecutive to ∠1, ∠2 and ∠3, respectively.

Hence,

• ∠1 + ∠4 = 180°   ……(i)
• ∠2 + ∠5 = 180°  …..(ii)
• ∠3 + ∠6 = 180°  …..(iii)

If we add the above three equations, we get;

∠1+∠2+∠3+∠4+∠5+∠6 = 180° + 180° + 180°

Now, by angle sum property we know,  

∠1+∠2+∠3 = 180°

Therefore,  

180 + ∠4+∠5+∠6 = 180° + 180° + 180°

⇒ ∠4+∠5+∠6 = 360°

This proves that the sum of the exterior angles of a triangle is equal to 360 degrees.