 Hello and welcome to the session. In this session we discussed the following question which says, in a triangle PQR, if 3 times angle P is equal to 4 times angle Q is equal to 6 times angle R, calculate the angles. Before moving on to the solution, let's recall the angles and property of a triangle. According to this property we have, that the sum of the angles of a triangle is 180 degrees. This is the key idea that we use in this question. Let's see the solution now. Consider this triangle PQR in which we have 3 times angle P is equal to 4 times angle Q is equal to 6 times angle R. Let this be equation 1. Now using the angles and property in triangle PQR we have in triangle PQR, angle P plus angle Q plus angle R is equal to 180 degrees. Let this be equation 2. Now from equation 1 consider 3 times angle P is equal to 6 times angle R. So this means angle P is equal to 6 upon 3 times angle R which means that angle P is equal to 2 times angle R. Now consider 3 times angle Q is equal to 6 times angle R from equation 1. So this gives us angle Q is equal to 6 upon 4 times angle R. Now 2 times is 4, 2 3 times is 6. So this gives us angle Q is equal to 3 upon 2 times angle R. Now using these values of angle P and angle Q in equation 2 we get this angle R plus 3 upon 2 times angle R plus angle R is equal to 180 degrees. This means 9 upon 2 times angle R is equal to 180 degrees or you can say that angle R is equal to 180 degrees into 2 upon 9. Now 9 20 times is 180 so angle R is equal to 20 into 2 that is 14 degrees. So we have got the value for angle R. Now we know angle P is equal to 2 times angle R so we get angle P equal to 2 into 40 degrees equal to 80 degrees. Therefore the value for angle P is 80 degrees. Now angle Q is equal to 3 upon 2 times angle R. So putting the value for angle R as 40 degrees we get angle Q is equal to 3 upon 2 into 40 degrees. Now 2 20 times is 40 so this is equal to 3 into 20 degrees equal to 60 degrees. Therefore we get angle Q is equal to 60 degrees. Thus we get angle P equal to 80 degrees, angle Q equal to 60 degrees and angle R equal to 40 degrees. This is our final answer. This completes the session. Hope you have understood the solution of this question.