 Hello and welcome to the session. In this session we discussed the following question which says the sum of the two angles of a triangle is equal to the third angle show that the triangle is a right triangle. We know that a triangle, one of whose angles measure 90 degrees is called a right triangle. This is the key idea for this question. Now we move on to the solution. Consider this triangle PQR. Now since we know that the sum of the angles of a triangle is 180 degrees therefore angle P plus angle Q plus angle R is equal to 180 degrees. Let's take this equation as equation 1. Now according to the question we have that the sum of the two angles of a triangle is equal to the third angle. So we take angle Q plus angle R is equal to the third angle which is angle P or we can say angle P is equal to angle Q plus angle R let this be equation 2. Now adding angle P to both sides of equation 2 we get angle P plus angle P is equal to angle P plus angle Q plus angle R this means 2 times angle P is equal to angle P plus angle Q plus angle R. So this means we get 2 times angle P is equal to 180 degrees from equation 1 since we know that angle P plus angle Q plus angle R is equal to 180 degrees. So this means angle P is equal to 180 degrees upon 2 which is equal to 90 degrees. So we get this angle P is of measure 90 degrees that is one angle of triangle P Q R is of measure 90 degrees therefore triangle P Q R is a right triangle as we know that if one of the angles of a triangle measure 90 degrees and it is called a right triangle. So hence proved this completes the session hope you have understood the solution for this question.