Answer :

(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}

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