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In trapezium ABCD, AB ∥ DC and AD = DC. If ∠DAB = 76°, find ∠DCA.

Class 8Kites and TrapeziumsQuadrilaterals
  • A76°
  • B52°
  • C38°
  • D104°

Step-by-Step Solution

Triangle ADC is isosceles (AD = DC), so ∠DAC = ∠DCA. Also ∠DCA = ∠CAB (alternate angles). So AC splits ∠DAB into two equal parts: ∠DCA = 76° ÷ 2 = 38°.
Answer: C) 38°

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