 Hi and welcome to the session. Let's work out the following question. The question says from figure find angle RTQ and angle RQT. So let us start with the solution to this question. First of all, let us name this angle at this 45 degree angle as angle 1, this angle as angle 2, this as angle 3, this as angle 4, this as angle 5 and 140 degree angle as angle 6. Now in the given figure, we see that angle 5 plus angle 6 should be equal to 360 degree because this is a central angle. Now it's given to us that angle 6 is 140 degree. So this implies angle 5 plus 140 degree is equal to 360 degree. This implies angle 5 is equal to 360 degree minus 140 degree that is equal to 220 degree. Now we know that angle 5 is twice of angle 2 because the angle subtended by an arc is twice the angle subtended by it on the circumference in alternate segment So this is how we have angle 5 is twice of angle 2. Now measure of angle 5 is 220 degree. So 220 degree is twice of angle 2 and this implies angle 2 is equal to 220 divided by 2 that is 110 degrees. Now angle 4 is exterior angle of cyclic quadrilateral PQ Tf therefore angle 4 will be equal to angle 2 because exterior angle of cyclic quadrilateral is equal to interior opposite angle. Therefore angle 4 is equal to angle R QT that is equal to 110 degree. Similarly angle 3 is equal to angle 1 that is this angle is equal to angle 1 angle 3 is angle RTQ that is equal to 45 degree. So our answer to this question is that angle RTQ is equal to 45 degree and angle R QT is equal to 110 degree. So I hope that you understood the solution and enjoyed the session. Have a good day.