In the given figure, AB = DB and AC = DC. If ∠ABD = 58°, ∠DBC = (2x - 4)°, ∠ACB = y + 15° and ∠DCB = 63°; find the values of x and y.

In △ ABC and △ DBC,

⇒ AB = DB (Given)

⇒ AC = DC (Given)

⇒ BC = BC (Common side)

∴ ∆ ABC ≅ ∆ DBC (By S.S.S. axiom)

We know that,

Corresponding parts of congruent triangles are equal.

∴ ∠ACB = ∠DCB

⇒ y + 15° = 63°

⇒ y = 63° - 15° = 48°.

From figure,

⇒ ∠ABC = ∠DBC = (2x - 4)° (By C.P.C.T.C.)

⇒ ∠ABC + ∠DBC = ∠ABD

⇒ (2x - 4)° + (2x - 4)° = 58°

⇒ (4x - 8)° = 58°

⇒ 4x = 58° + 8°

⇒ 4x = 66°

⇒ x = $\dfrac{66°}{4}$ = 16.5°.

Hence, x = 16.5° and y = 48°.