question_answer

In a quadrilateral PQRS, \[\angle \mathbf{P}:\angle \mathbf{Q}:\angle \mathbf{R}:\angle \mathbf{S}=\mathbf{2}:\mathbf{3}:\mathbf{3}:\mathbf{2}.\]Then  QRS is a ______

A)  Parallelogram                 

B) Isosceles trapezium

C)  Rectangle         

D)  square

Correct Answer: A

Solution :

(a): Let angles be \[2x,3x,3x,2x\] \[\Rightarrow 2x+3x+3x+2x={{360}^{{}^\circ }}\] \[\Rightarrow 10x={{360}^{^{0}}}\Rightarrow x={{36}^{{}^\circ }}\] \[\Rightarrow \] angles are \[{{72}^{{}^\circ }},{{108}^{{}^\circ }},{{108}^{{}^\circ }},{{72}^{{}^\circ }}\]