In the given figure BC is produced on both sides to points D and E respectively. Find the values of x and y.

In the figure, DCE is a straight line.

At point B, the angles ∠ABD and ∠ABC form a linear pair.

∴ ∠ABD + ∠ABC = 180°

We know from the figure that ∠ABD = x° and ∠ABC = 115°

Substituting the values in above, we get:

⇒ x + 115° = 180°

⇒ x = 180° - 115°

⇒ x° = 65°

At point C, the angles ∠ACB and ∠ACE form a linear pair.

∴ ∠ACB + ∠ACE = 180°

We know from the figure that ∠ACB = y° and ∠ACE = 132°

Substituting the values in above, we get:

⇒ y° + 132° = 180°

⇒ y° = 180° - 132°

⇒ y° = 48°

The values are x° = 65° and y° = 48°.