 Hello and welcome to another problem solving session on triangles in the given problem It has been given that angle X is 62 degrees. So you can see that in your Screen, so this angle is 62 degrees. It's given and XYZ is 54 So it's clearly, you know, this angle is 54 If why you and ZOR by sectors of XYZ and XY respectively? So this YO this line here bisects angle Y. So you can say that this angle is X So this angle also is X Similarly, OZ bisects XY. So if this is Y, this is Y. I hope this is clear Now you have to do what find OZ Y. So OZ Y that is Y itself small Y itself and X Z Y X Z Y is X Z Y that means sorry not X XY Y OZ So these are the angles I have to find out OZ Y Y OZ Let's try and find out So solution how to solve this problem again angles are given triangle is there. We know what is this Angle some property of a triangle. That's it. Mostly it will be done by that so some of three angles of a triangle is 180 degrees that we know so what all relations can we write so as you see I have taken variables X and Y so That will help me in writing the equations very easily. So what all equations can I write? Let's see. So on what is given for that matter. So if you check X is 54. No, sorry to X is 54 degrees 2 X is 54 degrees. So X is clearly 27 degrees Half of 54 no doubt about it. Now if I write Angle XYZ Plus angle Y Z X Plus angle X Z What why now the third angle is X itself that is Y X Z right if three angles are there X Y Z Y Z X and Y X Z right all put together is 180 degrees and why is this This is because of linear pair. Oh, sorry my bad not linear pair. This is because of angle some property angle some property of That triangle that is it. That's it. Right. So XYZ XYZ check it is to X Y Z X check it is to Y and Y X Z is 62 degrees and this is equal to 180 degrees Isn't it? So friends 2 X any ways we found out is 54 degrees. So 54 plus 2 Y plus 62 is equal to 180 degrees So this implies How much is 54 plus 62 6 and 1 1 6 degrees, right? So Yeah, and this 2 Y is 180 degrees So from here, you can calculate Y very easily. So 2 Y is equal to 180 degrees Minus 1 1 6 degrees Right. So this implies 2 Y is equal to 64 degrees Right and hence Y is 64 upon 2 That means 32 degrees Right. So dear friends Y is 32 degrees. That's what we wanted to find out. Oh Z Y isn't it? So Y has been found out now X is known Y is known, right? So I can mention here X is how much how much did we calculate? This is 27 and this Y is equal to 32 Right. So hence let's find out What is left to be found out now? Y o Z. So they're asking us to find out this angle Y o Z so clearly angle Y o Z plus X plus Y is 180 degrees and again, what is the reason? angle some property of a Triangle some is 180 degrees always. So why o Z will be So let's rise tried the values Y o Z is equal to 180 degrees minus X minus Y So 180 degrees minus X is 30. Sorry, 27 degrees minus 32 degrees. So 180 degrees minus 59 degrees isn't it? And hence this is how much 121 degrees. So we found out this angle to be equal to 121 degrees. So all done. Correct. This is what the problem was asking us to find out. So basically we applied only angles and property of the triangle to solve this problem.