In the figure, ABCD is a parallelogram in which ∠ADC=105∘. The value of ∠CBE is ______.
A
105∘
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B
75∘
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C
55∘
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D
90∘
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Solution
The correct option is B75∘
ABCD is a parallelogram Therefore, ∠ADC=∠ABC=105∘[Opposite angles of a parallelogram are equal] ∠ABC+∠CBE=180∘ [Linear pair] ∠CBE=180∘−105∘=75∘ Hence, ∠CBE=75∘.