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 55^o are vertically opposite angles

Therefore,

∠x = 55^o

Also,

∠x and ∠y form a linear pair

Therefore,

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

55^o + ∠y = 180^o

∠y = 180^o – 55^o

= 125^o

Also,

∠y and ∠z are vertically opposite angles

Therefore,

∠y = ∠z = 125^o

Hence,

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

∠x = 55^o

∠y = 125^o

And,

∠z = 125^o

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

We have,

∠z and 40^o are vertically opposite angles

Therefore,

∠z = 40^o

Also,

∠y and ∠z form a linear pair

Therefore,

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

∠y + 40^o = 180^o

∠y = 180^o – 40^o

= 140^o

Also, we know that:

Sum of angles in a straight line = 180^o

∠x + 40^o + 25^o = 180^o

∠x + 40^o + 25^o = 180^o

∠x + 65^o = 180^o

∠x = 180^o – 65^o

= 115^o

Hence,

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

∠x = 115^o

∠y = 140^o

∠z = 40^o