Question

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

Answer 1

Let the angles of a triangle be x,y and z degrees

Therefore, let the exterior angle formed by one of the sides = 180-x degree

As we know,

Sum of the interior angles of a triangle = 180 degree

x+y+z = 180

y+z = 180-x degree

As we see,

Exterior angle formed by one of the sides = y+z

Therefore we can say that,

Exterior angle = sum of the opposite two interior angles

Hence, proved

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