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      Question

      In a quadrilateral PQRS, the bisectors of ∠R and ∠S

      intersects each other at point 'O'. Find the ∠Q if ∠P = 75o and ∠ROS = 95o.
      A 115° Correct Answer Incorrect Answer
      B 95° Correct Answer Incorrect Answer
      C 105° Correct Answer Incorrect Answer
      D 125° Correct Answer Incorrect Answer

      Solution

      Image
      In ΔROS;

      We have, ∠ROS + ∠ORS + ∠OSR = 180o

      Or, 95o + ∠ORS + ∠OSR = 180o

      Or, ∠ORS + ∠OSR = 85o

      Or, (∠R/2) + (∠S/2) = 85o {∠ORS = (∠R/2) and ∠OSR = (∠S/2) }

      So, ∠R + ∠S = 170o

      We know that sum of each angle of a quadrilateral is 360o.

      So, ∠P + ∠Q + ∠R + ∠S = 360o

      Or, 75o + ∠Q + 170O = 360o

      Or, ∠Q = 360o - 245o

      So, ∠Q = 115o

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