 Hello, and welcome to the session. Today we will discuss the following question which says in figure pq is equal to 24 centimeters, qr is equal to 26 centimeters, angle par is equal to 90 degrees, pa is equal to 6 centimeters and ar is equal to 8 centimeters, fine angle qpr. Before moving on to the solution let's recall that in a triangle if square of one side is equal to the sum of the squares of the other two sides then the angle opposite the first side is a right angle. This will be the key idea for this question. Now let's move on to its solution. We are given that pq is equal to 24 centimeters, qr is equal to 26 centimeters, angle par is equal to 90 degrees, pa is equal to 6 centimeters and ar is equal to 8 centimeters and we need to find angle qpr. So here we need to find angle qpr which is this angle. Here first of all we are given that angle par is 90 degrees that is a right angle that means triangle apr is a right angle to triangle. So in right triangle apr, pr will be the hypotenuse. So we have pr square is equal to pa square plus ar square by Pythagoras theorem substituting the values of pa and ar we get pr square is equal to pa square that is 6 square plus ar square that is 8 square centimeter square which will be equal to 36 plus 64 centimeter square that is 100 centimeter square thus pr will be equal to 10 centimeters. So here we have pr equal to 10 centimeters. Now consider the triangle qpr. So in triangle qpr we have qp equal to 24 centimeters that means qp square will be equal to square of 24 centimeters which will be equal to 576 centimeter square. Now qr is equal to 26 centimeters. So qr square will be equal to square of 26 centimeters that is 676 centimeter square and lastly pr is equal to 10 centimeters. So pr square will be equal to square of 10 centimeters that is 100 centimeter square. Now if you notice all these three figures then you will find that 676 centimeter square is equal to 576 centimeter square plus 100 centimeters square. So this implies that qr square is equal to qp square plus pr square that is the square of one side of the triangle qpr that is qr square is equal to the sum of the squares of other two sides that is qp square plus pr square and in key idea we have learned that in a triangle if a square of one side is equal to the sum of the squares of other two sides then the angle opposite to the first side is a right angle. So that means angle opposite to the side qr will be right angle and the angle opposite to the side qr is angle qpr that means angle qpr is the right angle that is 90 degrees. Thus angle qpr is equal to 90 degrees and we were supposed to find out the measure of angle qpr. So angle qpr equal to 90 degrees is the required answer. With this we finished the session. Hope you must have enjoyed it. Goodbye, take care and keep smiling.