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.
Solution
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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