Question

Prove that the sum of three exterior angles of a triangle formed by producing the sides in order is four right angle of 360 degree.

Answer 1

Step-by-step explanation:

consider aΔABC

∠y=∠1+∠3... (i) (due to ext. angle property)

and ∠z=∠1+∠2... (ii) (due to ext. angle property)

also ∠x=∠2+∠3... (iii) (due to ext. angle property)

Adding equation (i), (ii) and (iii), we get

∠x+∠y+∠z=∠1+∠3+∠1+∠2+∠2+∠3

⇒∠x+∠y+∠z=2∠1+2∠2+2∠3

⇒∠x+∠y+∠z=2(∠1+∠2+∠3)=2×180° = 360°

Hence, ∠x+∠y+∠z=4 right angles

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.