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ABCD is a rhombus. If ∠BAC = 38°, find :

(i) ∠ACB

(ii) ∠DAC

(iii) ∠ADC.

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#### Solution

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 = `1/2` [180° - 104°]

∠DAC = `1/2 xx` 76° = 38°

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

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