Question

Sum of interior angle of triangle is equal to exterior angle prove

Answer 1

Answer:

In triangle ABC Bc is produced to

D. LA+LB =LACD

LA+LB+LACB=l80, LA+LB = 180-LACB

LACB+LACD=180

from this Sum of intr.Lequal to

ExtrL Proved

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.