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ICSE-VIII-Mathematics

17: Special Types of Quadrilaterals Class 8 Maths

with Solutions -
Qstn# A-6 Prvs-QstnNext-Qstn
  • #6
    ABCD is a rhombus. If ∠BAC = 38°, find : (i) ∠ACB (ii) ∠DAC (iii) ∠ADC.
    Ans : 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 x 76° = 38°
    Hence (i) ∠ACB = 38° (ii) ∠DAC = 38° (iii) ∠ADC = 104°