 Hey, hello friends welcome again to another problem-solving session on triangles the good given question says if pq is perpendicular to ps. Let's identify that so if you see This is perpendicular here. This angle is 90 degrees pq is perpendicular to ps Pq is parallel to sr. Also, so this these two lines are parallel and Sqr is 28 degrees. So this angle is sqr 28 degrees. It's given qr T is 65. So this angle is given 65 Then find the values of x and y. So this x and here is y. We have to find these two values so again, we will go by whatever we have learned and mostly the sum of three angles of a triangle that is angles some property and Exterior angle theorem both these Would be applicable. Let's see how so What else is given so if you see Let's start with Yeah, so solution so if you see given is pq parallel to sr What does that mean that means? Angle q ps plus angle psr It will be equal to 180 degrees and why is that consecutive interior angles co-interior angles so consecutive interior angles of a Transversal is it? consecutive interior angles on a transversal or offer transversal. What is the transversal here? Transversal here is this line ps This line ps is a transversal pq and sr are parallel lines. So clearly this angle Because this angle will be 180 degrees. That's what I have written so I Can find now? Q ps is given to be 90 degrees right now. So hence 90 degrees Plus psr is 180 degrees that means Angle psr can be easily found out and that is nothing but 180 degrees minus 90 degrees So 90 degrees So psr is also 90 degrees. Let me Show it like that Okay, so if that is 90 degrees Now if I somehow find out qsr then I can find out why so let's try to find out qsr qsr is this angle so what I'm going to say is angle qrt angle qrt is equal to angle qsr Plus angle q angle sqr and why is that? This is because of external angle theorem external angle Theorem and what is that theorem? That theorem says that external angle this angle will be equal to sum of interior opposite angles. That means this one and This one my thing, right? So let me write it here now. So Yeah, what do I get from here? So I get 65 degrees that is qrt is equal to 28 degrees Plus angle qsr. Is it it? So I will get qsr from here. This implies qsr angle qsr is how much? 65 degrees minus 28 degrees, which is nothing but 37 degrees Isn't it? So I got q sr s 37 degrees. So what is why? Why will clearly be? So you can now find out why for that matter before finding out why if you see angle qsr is equal to angle Pq y Pq y which is equal to sorry Pq s not y Pq s Pq s and that is equal to x and y is this. This is because of alternate interior Angle of two parallel line. Isn't it? Pq is parallel to sr So clearly this angle and this angle are same alternating interior. So this will be x as well Right. So we got xn. This is equal to Nothing but 37 degrees. So x is 37 degrees Now x plus y is 90 degrees. See from the figure x plus y if this angle is x this angle is x This angle is y. So x plus y is 90 degrees x I have already found out. So y will be simply 90 degrees minus x Right, which is equal to 90 degrees minus 37 degrees Which will give you 53 degrees. So y is 53 degrees, right? So you could find out x is 37 and y is 53 degrees. That is how you Solve the problem. So the two things which we learned or which we used here is again angle some property So wherever there is a triangle and angles are involved. So angle some property will come handy and And secondly is exterior angle theorem. Exterior Angle theorem sum of two interior opposite angle is equal to the exterior angle. That is something which we need to Apply, right? I hope you understood the problem