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If a perpendicular drawn from an obtuse –angled vertex of a rhombus to the opposite side bisects the side ,find all the angles of the rhombus.

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Let the acute angle be A and obtuse angle be B.

Rhombus ABCD, and angle A = angle C = acute angles.

The perpendicular from B to AD be BE.

Now in ΔABE, AE = ED = AB/2 = AD/2

cos A = AE/AB = 1/2

angle A = 600 = angle C 

angle B = angle D = (360 - 2x60)/2 = 1200.

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