 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says it is given that angle x y z is equal to 64 degree and x y is reduced to a point p draw a figure from the given information if ray y q by 6 angle z y p find angle x y q and reflects angle q y p. So, let us begin with the solution and first let us draw a figure with the given information given that x y is produced to a point p it implies x p is a line. It has been a required line and also we are given that angle x y z is equal to 64. So, we have taken a point y on line x p and then drawn angle x y z as 64 degree. So, this is the required figure now we are further given that ray y q by 6 angle z y p. So, let us draw a ray y q which by 6 this angle this is the required ray and these two angles are equal since y q by 6 angle p y z. Now, since y z stands on x p x p is a line therefore we must have angle x y z plus angle p y z is equal to 180 degree since they form a linear pill. Angle x y z is equal to 64 degrees plus angle p y z as it is equal to 180 degree this implies that angle p y z is equal to 180 degree minus 64 degree it is equal to 160 degree plus we have angle p y z is equal to 116 degree. Now, since we are given that y q by 6 angle p y z therefore p y z which is the sum of two angles p y q and q y z can be further written as angle p y q plus angle p y q which is equal to 116 degree. So, this implies two times of angle p y q is equal to 116 degree which further implies that angle p y q is equal to 116 degree which is equal to 16 upon 2 which is equal to 58 degree. So, we have angle p y q is equal to 58 degree or we can also say angle q y p is equal to 58 degree. To find the reflex of angle q y p we will subtract angle q y p from 360 degrees which is equal to 302 degree thus we have reflex angle q y p is equal to 302 degree. Now let us find angle x y q which is the sum of angle x y z and angle z y q. So, angle x y q can be written as sum of angles x y z and angle z y q. x y z is equal to 64 degree and z y q is equal to 58 degree since line y q bisectangle p y z therefore both these angles will be of 58 degree. So, z y q is 58 degree. Now on adding we get 122 degree. So, we have angle x y q is equal to 122 degree thus and answers are angle x y q is equal to 122 degree and reflex angle q y p is equal to 302 degree. So, this completes the solution. Hope you enjoyed it. Take care and bye for now.