ABCD is a rhombus with ∠ABC = 126°, find the measure of ∠ACD.
A
27°
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B
63°
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C
90°
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D
153°
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Solution
The correct option is A 27° ∠ABC = ∠ADC (Opposite angles of a rhombus)
∠ADC = 126°
∠ODC = 12 × ∠ADC (Diagonal of rhombus bisects the respective angles)
⇒ ∠ODC = 12 × 126° = 63°
⇒ ∠DOC = 90° (Diagonals of a rhombus bisect each other at 90°)