Question

prove that sum of angle of a triangle is 180​

Answer 1

Draw a ray parallel to the base of the triangle, use the theorem of alternate interior angles to compare angles of triangles and prove then equal to the total of the angles of a straight line (180 degrees)

Answer 2

Proof that the sum of the angles in a triangle is 180 degrees

Theorem

If ABC is a triangle then <)ABC + <)BCA + <)CAB = 180 degrees.

Proof

Draw line a through points A and B. Draw line b through point C and parallel to line a.

triangle

Since lines a and b are parallel, <)BAC = <)B'CA and <)ABC = <)BCA'.

It is obvious that <)B'CA + <)ACB + <)BCA' = 180 degrees.

Thus <)ABC + <)BCA + <)CAB = 180 degrees.