 Hello friends, and how are you all doing today? The question says in figure O is the center of the circle if Angle CEA is equal to 30 degrees find the values of X Y and Z Now we are given the figure like this. We need to find out the value of X that is in the figure Here X Y and Z provided. We are given angle CEA Equal to 30 degrees now. Let us start with our solution We are given that O is the center of the circle and Angle CEA is equal to 30 degrees This is what is given to us in the question. We need to find the values of X Y and Z So let us start with our proof Since angle CEA is equal to 30 degrees So we can write that therefore angle CDA is also equal to 30 degrees as it is The angle in the same Segment that is AC on segment AC There are two angles which are made that are CEA as well as CDA, right? Further We are given that since O is the center of the circle therefore we can say that Angle Y is equal to twice angle CD because Angle subtended by an arc That is AC arc AC that we are talking about in the question at the center and At the center the angle which is subtended by arc AC is angle Y is double the angle subtended by It that is the arc AC at any point on the remaining of the Circle so as we can see that The angle which is made by this arc AC on the remaining part of the circle is angle CEA as well as angle CDA so angle Y is Double angle CDA which is equal to CEA so we have Therefore we can see that angle Y is equal to angle CDA Which is found above as 30 degrees so it is twice into 30 degrees Which is equal to 60 Degrees and lastly we need to find out angle X to we know that ABCO is a Quadrilaterals that is forming over here therefore We can say that Angle X plus angle Y is equal to 180 degrees because The sum of Opposite angles of a quadrilateral is 180 Degrees we have the value of angle Y as 60 above so we have angle X plus 60 degree equal to 180 degrees Therefore angle X is equal to 180 degrees minus 60 degrees Which implies the value of X is coming out to be 120? degrees so in the answer we can write down that Angle X Angle Y and angle Z are having Angles as 120 degrees 60 degrees and 30 degrees respectively Right, so this completes the session. Hope you understood the whole concept well and the question to have a nice day ahead