In a parallelogram ABCD, ∠A - ∠C is


Answer:



Step by Step Explanation:
  1. Following figure shows the parallelogram ABCD,

    We know that opposite sides of parallelogram are parallel, therefore AB || DC and AD || BC.
  2. Let's draw AC, such that parallel lines AB and DC are intersected by transversal AC. Therefore,
    ∠CAB = ∠ DCA ............ (Interior alternate angles)
  3. Similarly, parallel lines AD and BC are intersected by transversal AC. Therefore,
    ∠ACB = ∠ DAC ............ (Interior alternate angles)
  4. Now,
      ∠A - ∠C = (∠CAB + ∠DAC) - (∠DCA + ∠ACB)
    ⇒ ∠A - ∠C = (∠CAB - ∠DCA) + (∠DAC - ∠ACB)
    ⇒ ∠A - ∠C = 0 + 0 .... (since ∠CAB = ∠ DCA and ∠ACB = ∠ DAC)
    ⇒ ∠A - ∠C = 0

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