In figure (3) given below, ABCD is a rhombus. Find x and y.

Sides of rhombus are equal.

∴ AB = AD

⇒ 4x - 4 = 3x + 2

⇒ 4x - 3x = 2 + 4

⇒ x = 6.

AB = 3x + 2 = 3(6) + 2 = 20.

In △ABD,

AB = AD

so, ∠D = ∠B (Angles opposite to equal sides are equal in isosceles triangle)

Let angle be ∠D = ∠B = a

So,

⇒ ∠A + ∠D + ∠B = 180°

⇒ 60° + a + a = 180°

⇒ 2a = 180° - 60°

⇒ 2a = 120°

⇒ a = 60°.

Hence, △ABD is an equilateral triangle, so all sides are equal.

⇒ BD = AB

⇒ y - 1 = 20

⇒ y = 21.

Hence x = 6 and y = 21.