 Hello and welcome to problem solving session on triangles Now the question says in the given figure Q2 Qt is perpendicular to PR. So let's understand the figure first So it's given that Qt is perpendicular to PR correct and what else TQR is 40 degrees. So you can see TQR is 40 degree here 40 degree and SPR is 30 degrees. So this is 30 degrees. We have to find out X and Y So convention is to write first given what is given. So all that Mentioned in the problem Q2 is perpendicular to PR and Angle TQR is 40 degrees and Angle SPR is 30 degrees. Okay to find what do we need to find? We need to find values of X and Y. Okay, so in triangle we know That the sum of three angles is 180 degrees and since in this given figure We have been asked to find out the values of X and Y which happen to be Angles themselves. So let's use the known fact that is sum of three angles of Triangle is 180 degrees and second one which is going to be used is Exterior angle theorem that is the sum of Interior opposite angles is equal to the exterior angle. These are the two things which we are going to use So let's solve this problem now If you see angle since since Qt is perpendicular to PR, okay therefore Cannot say that Qtp is 90 degrees a right angle Correct Qtp is right angle now if you notice this Qtp is the exterior angle Exterior angle and the interior opposite angles are these two. This one is one This one is two, isn't it? So guys, can I not say that angle Qtp is equal to Angle TQR Plus X and why can I say this? This is because Exterior angle theorem Isn't it? Right, exterior angle theorem Very well. So Qtp is 90 degrees. We already know so 90 degrees TQR is 40 degrees. So 40 degrees plus X So very very straightforward now. So what is X? X is 90 degrees minus 40 degrees Which is 50 degrees. So we got the value of X. Now, let's find out the value of Y So again, if you look closely For Y if this is Y this angle is this Y. This is Y Then interior angles are X and this 30 degree, isn't it? For that triangle or that angle P sq. So I'm saying Angle P sq is equal to Angle SPR Plus Angle PRS Is it? Why is this again? because of Exterior Angle theorem Sum of interior opposite angles is Exterior Angle. Correct. So P s Q Right, so that is Y. So Y will be equal to 30 degrees plus X Because SPR was 30 degree you can see from the figure and X we just found out which was 50 degrees So it becomes 30 plus 50 degrees hence Y is 80 degrees, right? So that's how we found out both X and Y. So X is 50 and so to summarize X is equal to 50 degrees and Y is 80 degrees. So we did not require The angles some property in this case Is it it? You could have used it if let's say the question and asked you to find out this angle Right, then angle some property would be used. So let's say this vertically opposite angles if you have to find out Then angle some property could have been used. Okay