In the figure- ABCD which - ADC -105- - CBE isA- 55-B- 105-C- 75-D- 90-

The correct option is C ABCD is a parallelogram Therefore, ∠ ADC=∠ ABC=105^∘[ Opposite angles are equal] ∠ ABC+∠ CBE=180^∘ [Linear pair] ∠ CBE=180^∘ ∠ ABC ∠ C ...

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Standard VI

Mathematics

Parallelogram

In the figure...

Question

In the figure, ABCD is a parallelogram in which $∠ A D C = 105^{\circ}, ∠ C B E$ is

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Solution

The correct option is B
ABCD is a parallelogram

Therefore, $∠ A D C = ∠ A B C = 105^{\circ}$ [ Opposite angles are equal]
$∠ A B C + ∠ C B E = 180^{\circ}$ [Linear pair]
$∠ C B E = 180^{\circ} - ∠ A B C$
$∠ C B E = 180^{\circ} - 105^{\circ} = 75^{\circ}$
Hence, $∠ C B E = 75^{\circ}$

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