Abcd Is Rhombus If В€ Bac 38в° Find В€ Acb

ABCD is a rhombus. If ∠BAC = 38°, find : (i) ∠ACB (ii) ∠DAC (iii) ∠ADC.

Answers:

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 = $\frac { 1 }{ 2 }$ [180° – 104°]
∠DAC = $\frac { 1 }{ 2 }$ x 76° = 38°
Hence (i) ∠ACB = 38° (ii) ∠DAC = 38° (iii) ∠ADC = 104°