Question

prove that all angle of the triangal sum is 180​

Answer 1

     

Hey mate!!!

Nice question!!!

Consider the triangle ABC in the figure. The circle is the circumcircle of the triangle ABC and O is the circumcenter of the triangle. OA, OB and OC are circumradii such that OA = OB = OC. The sides of the triangle AB, BC and AC are the chords of the circumcircle.

Here, ∠AOC = 2∠ABC,  ∠BOC = 2∠BAC  &  ∠AOB = 2∠ACB

   

And,

⇒ ∠AOC + ∠BOC + ∠AOB = 360°

⇒ 2∠ABC + 2∠BAC + 2∠ACB = 360°

⇒ 2(∠ABC+ ∠BAC + ∠ACB) = 360°

⇒ ∠ABC+ ∠BAC + ∠ACB = 180°

Hence proved that the sum of angles in any triangle is 180°!!!

Thank you...

$\mathfrak{\#adithyasajeevan}$