Prove that a side of a triangle produced the exterior angle, so formed is equal to the sum
of the two interior opposite angles .
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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.
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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.
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