ABCD is a cyclic quadrilateral which sides AD and BC are produced to meet at P, and sides DC and AB meet at Q when produced. If ∠ A = 60o and ∠ ABC = 72o, then ∠ PDC - ∠ DPC = ?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 24o
Explanation:
In ∠ABP,
∠A + ∠ABC + ∠APB = 180o
⇒ ∠APB = 180 - 60 - 72 = 48o
⇒ ∠ADC = 180 - ∠ABC = 180 - 72 = 108o
⇒ ∠PDC = 180 - ∠ADC = 180 - 108 = 72o
Hence
∠PDC - ∠DPC = 72 - 48 = 24o