Prove the triangle sum theory

Question

Triangle Sum Theorem: The three angle measures of a triangle add to 180°. Goal: To prove m∠1 + m∠2 + m∠3 = 180°

Answer 1

If you draw any parallelogram you can show that the sum of it’s angles is 360 as it consists of 2 pairs of consecutive angles; consecutive angles are supplementary(2 x 180 =360)

Now draw a diagonal and prove that is divides the parallelogram into 2 congruent triangles by SSS

So the sum of the angles of each triangle will be one half of 360=180

Answer 2

Theorem , proven by induction, states that the sum of the interior angles of the regular N-gon is

(N-2)*180.

For N=3, (3-2)*180 = 180.

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