Question

If in a rhombus ABCD, angle A = 72 degrees, then angle D =

Answer 1

opposite angles of rhombus are equal

=> ∠ADC = ∠ABC

given ∠ABC =  72°

=> ∠ADC =  72°

All sides of rhombus are equal

hence ΔADC is isosceles triangle

AD = CD

=> ∠CAD = ∠ACD

∠CAD + ∠ACD + ∠ADC = 180° ( sum of angles of triangle)

=> ∠CAD + ∠ACD + 72° = 180°

=> ∠ACD + ∠ACD  = 108°

=> 2∠ACD  = 108°

=> ∠ACD  = 54°

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