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Given: ∠1 and ∠2 form a linear pair; ∠1 and ∠3 are supplementary
Prove: ∠2 = ∠3

Sagot :

varshamittal029

The statement "If ∠1 and ∠2 form a linear pair; ∠1 and ∠3 are supplementary, then ∠2 = ∠3" is proved.

If the sum of two angles is 180 then they are called supplmentary angles of each other.

If one straight line meets another straight line at a point, then two adjoint angles at that point on that line is called Linear angles to each other.

Here given that ∠1 and ∠2 are linear to each other.

From property of the linear angles we know that the sum of linear angles is 180.

Therefore, ∠1 + ∠2 = 180

So, ∠2 = 180 - ∠1 .........(1)

Also it is given that, ∠1 and ∠3 are supplementary angles.

So, ∠1 + ∠3 = 180

Therefore, ∠3 = 180 - ∠1.....(2)

Comparing (1) and (2) we get,

∠2 = ∠3 = 180 - ∠1

Therefore, ∠2 = ∠3, proved

Learn more about Supplementary Angles here -

https://brainly.in/question/24782288

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