Question

using mathematical induction.show some of the measure of three angles of a triangles is 180??

Answer 1

Let us prove it by induction.

Let us assume that a polygon with 'n' sides has some of the measures of all the angles as $(n-2) 180^\circ$.

We need to use this to prove that the same statement is true for a polygon with (n + 1) sides.

So, a polygon with (n+1) sides has $((n + 1) - 2) \times 180^\circ= (n - 1) \times 180^\circ$ degrees.  

Therefore, the polygon with 'n' vertices has $(n - 2) \times 180^\circ$ degrees as the sum of its angles by the inductive assumption. The triangle has 180 degrees as the sum of its angles. This means the triangle had 180 degrees as the sum of its angles, proving the inductive hypothesis.