 Hello and welcome to the session. In this session we discuss the following question that says in the given figure the bisectors of angle Q and angle R meet in a point P. If angle T is equal to 80 degrees and angle S is equal to 80 degrees find the measure of angle R P Q. Before moving on to the solution, let's recall the facts that the sum of the angles of a quadrilateral is 360 degrees and the sum of the angles of a triangle is 180 degrees. This is used as the key idea for this question. Now, let's move on to the solution. We have the quadrilateral. S, T, Q, R. In this we are given angle T is equal to 80 degrees and angle S is equal to 80 degrees. It's given that Q P is the bisector of angle Q and R P is the bisector of angle R. Now in this quadrilateral, S, T, Q, R we have angle S plus angle T plus angle Q plus angle R equal to 360 degrees since sum of the angles of a quadrilateral is 360 degrees. Now we know that angle S and angle T are given of measure 80 degrees. So we substitute these values for both the angles in this equation. So we get 80 degrees plus 80 degrees plus angle Q plus angle R equal to 360 degrees. This gives us 160 degrees plus angle Q plus angle R equal to 360 degrees. So from here we get angle Q plus angle R equal to 200 degrees. Now dividing both sides by two we get half of angle Q plus half of angle R equal to 100 degrees. Now we know that Q P is the bisector of angle Q. So half of angle Q can be taken as angle R Q P plus half of angle R can be taken as P R Q since R P is the bisector of angle R. So we have angle R Q P plus angle P R Q is equal to 100 degrees. Now in triangle P Q R we have angle R P Q plus angle R Q P plus angle P R Q is equal to 180 degrees since the sum of the angles of a triangle is 180 degrees. Now from this equation we have angle R Q P plus angle P R Q equal to 100 degrees. So we can substitute this in this equation. So this gives us angle R P Q plus 100 degrees is equal to 180 degrees. So this gives us angle R P Q is equal to 80 degrees. Thus our final answer is angle R P Q is equal to 80 degrees. So this completes the session. Hope you have understood the solution for this question.