In rhombus ABCD,angle A = angle B - 30^{circ} | vedclass

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Question

(A) In a rhombus $ABCD$,adjacent angles are supplementary,meaning $\angle A + \angle B = 180^{\circ}$.Given that $\angle A = \angle B - 30^{\circ}$,we

Vedclass · Accepted Answer

$75$

Vedclass · Answer

(A) In a rhombus $ABCD$,adjacent angles are supplementary,meaning $\angle A + \angle B = 180^{\circ}$.Given that $\angle A = \angle B - 30^{\circ}$,we can substitute this into the equation:$(\angle B - 30^{\circ}) + \angle B = 180^{\circ}$$2\angle B = 210^{\circ}$$\angle B = 105^{\circ}$.Since $\angle A = \angle B - 30^{\circ}$,then $\angle A = 105^{\circ} - 30^{\circ} = 75^{\circ}$.In a rhombus,opposite angles are equal,so $\angle C = \angle A$.Therefore,$\angle C = 75^{\circ}$.

In rhombus $ABCD$,$\angle A = \angle B - 30^{\circ}$,then $\angle C = \ldots$ (in $^{\circ}$)

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