Question

The given figure shows a rhombus ABCD in which angle BCD = 80°. Find angles x and y.

Answer 1

In rhombus ABCD, diagonals AC and BD bisect each other at 90°

∠BCD = 80°

Diagonals bisect the opposite angles also ∠BCD =

∠BAD (Opposite angles of rhombus)

∠BAD = 80° and ∠ABC = ∠ADC = 180° – 80° = 100°

Diagonals bisect opposite angles

∠OCB or ∠PCB =`80^circ/2` = 40°

In ∆PCM,

Ext. CPD = ∠OCB + ∠PMC

110° = 40° + x

⇒ x = 110° – 40° = 70°

and ∠ADO = `1/2` ∠ADC = `1/2 xx 100^circ = 50^circ`

Hence x = 70° and y = 50°