In Figure 5.63 two straight lines AB and CD are intersecting each other at point O and the angle thus formed at O are marked.

Here the value of ∠x – ∠y is –

Let the intersection point be O.

If we consider line AB, AB is a straight line. ∠ x + ∠ y forms a linear pair and in the similar manner ∠ AOD + 62° = 180°

Sum of all the angles about O is 360°.

∠ x + ∠ y + ∠ AOD + 62° = 360°

180° + ∠ AOD + 62° = 360°

∠ AOD + 242° = 360°

∠ AOD = 360 – 242

∠ AOD = 118°

Now ∠ y = 62° [vertically opposite angles]

Also ∠ x = ∠ AOD = 118° [vertically opposite angles]

So ∠ x - ∠ y = 118 – 62

= 56°

So the correct answer is A.