Question

ABCD is a rhombus. If <BAC =38°, find :
(a) <ACB
(b) <DAC
(c) <ADC

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Answer 1

Answer:

ABCD is Rhombus (Given)

AB = BC

∠BAC = ∠ACB (∠s opp. to equal sides)

But ∠BAC = 38° (Given)

∠ACB = 38°

In ∆ABC,

∠ABC + ∠BAC + ∠ACB = 180°

∠ABC + 38°+ 38° = 180°

∠ABC = 180° – 76° = 104°

But ∠ABC = ∠ADC (opp. ∠s of rhombus)

∠ADC = 104°

∠DAC = ∠DCA ( AD = CD)

∠DAC = ½ of [180° – 104°]

∠DAC = ½ x 76° = 38°

Hence (i) ∠ACB = 38° (ii) ∠DAC = 38° (iii) ∠ADC = 104°