Question

Prove that a side of a triangle produced the exterior angle, so formed is equal to the sum

of the two interior opposite angles .​

Answer 1

Step-by-step explanation:

Statement : If side of a triangle is produced, then the exterior angles so formed is equal to the sum of the two interior opposite angles. Given : A triangle ABC with interior angles x , y and z and exterior angle 'e'. Hence, it is proved.

Answer 2

Answer:

Statement : If side of a triangle is produced, then the exterior angles so formed is equal to the sum of the two interior opposite angles.

Given : A triangle ABC with interior angles x , y and z and exterior angle 'e'.

To prove : e = x + y

Proof :

In the figure, :

x + y + z = 180°.... (i) [Angle sum property]

e + z = 180 ° ........ (ii) [Linear pair]

On camparing equation ( i ) and ( ii )

x + y + z = e + z

Therefore, x + y = e

Hence, it is proved.