Question

prove that the exterior angles formed by producing one of the sides of a triangle is equal to the sum of the opposite interior angles
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Answer 1

Answer:

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Answer 2

Answer :

Given:

A triangle ABC

To prove :

The sum of two opposite interior angles of a triangle is equal to the exterior angle formed by producing one of the sides of triangle

Proof :

Let ABC a triangle on a segment AD

Now sum of Angle BCA and BCD is forming a linear pair which means that ,

= Angle BCA + Angle BCD = 180

Let this be equation 1

Also we know that the angle sum property of a triangle is 180 degree. So by this property now we have ,

= Angle BAC + Angle ABC + Angle BCA = 180

Let this is equation 2

Since , from equation 1 and 2 we have

Angle BCD = Angle BAC + Angle ABC

Hence it has been proved that the sum of two opposite interior angles of a triangle is equal to the exterior angle formed by producing one of the sides of triangle