Question

why is the sum of the interior angles of a triangle always 180.prove theoretically? please give me full process.

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

For the answer check the attachment .

Let ABC be a triangle .

Then draw a line DE such that DE║BC .

Then note that ∠CBA = ∠BAD (i) (Alternate Interior Angles)

Also ∠BCA = ∠CAE (ii) (Alternate Interior Angles)

And we have ∠BAD + ∠BAC + ∠CAE = 180° (Sum of all angles on a straight line is 180°)

By substituting ∠BAD and ∠CAE from (i) and (ii) , we get :-

=> ∠CBA + ∠BAC + ∠BCA = 180°.

Since ∠CBA , ∠BAC , ∠CAE are angles of the triangle , we proved that sum of all interior angles in a triangle are 180°.

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