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Question
If ABCD is a rhombus with ∠ABC = 56°, find the measure of ∠ACD.
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Solution
The figure is given as follows:
ABCD is a rhombus.
Therefore,
ABCD is a parallelogram.
Thus,
∠ABC =∠ADC
∠ADC = 56°[ ∠ABC = 56°(Given)]
∠ODC = 28 [`∠AODC = 1/2∠ADC`]
Now in ΔODC,we have:
∠OCD +∠ODC +∠COD = 180°
∠OCD + 28° + 90° = 18
∠OCD = 62°
∠ACD = 62°
Hence the measure of ∠ACDis 62° .
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