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