Find the values of the angles x, y and z in each of the following:

(i)


(ii)


(i) We have to find the value of x, y and z


We have,


x and 55o are vertically opposite angles


Therefore,


x = 55o


Also,


x and y form a linear pair


Therefore,


x + y = 180o (Sum of linear pair angles)


55o + y = 180o


y = 180o – 55o


= 125o


Also,


y and z are vertically opposite angles


Therefore,


y = z = 125o


Hence,


The value of x, y and z is as follows:


x = 55o


y = 125o


And,


z = 125o


(ii) We have to find out the values of x, y and z


We have,


z and 40o are vertically opposite angles


Therefore,


z = 40o


Also,


y and z form a linear pair


Therefore,


y + z = 180o (Sum of angles of linear pair)


y + 40o = 180o


y = 180o – 40o


= 140o


Also, we know that:


Sum of angles in a straight line = 180o


x + 40o + 25o = 180o


x + 40o + 25o = 180o


x + 65o = 180o


x = 180o – 65o


= 115o


Hence,


The value of x, y and z is as follows:


x = 115o


y = 140o


z = 40o


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