question_answer

In the adjoining figure, line P || line Q and line M and N are transversals. As per information in figure, find \[m\angle a+m\angle b\].  

A) \[225{}^\circ \]                     

B)           \[90{}^\circ \]

C) \[180{}^\circ \]                     

D)           \[170{}^\circ \]

Correct Answer: D

Solution :

      Since PR || QS \[\angle MAB=\angle ADC\] (Corresponding angles) \[\angle \,ADQ+\angle ADC={{180}^{\text{o}}}\] (Linear pair) \[\angle \,ADC={{180}^{\text{o}}}\,-{{110}^{\text{o}}}={{70}^{\text{o}}}\] \[\angle \,={{70}^{\text{o}}}\] \[\angle \,ABC=\angle \,NBR\] (Vertically opposite angles) = 100° Since PR || QS, \[\angle \,BCS=\angle \,ABC\] (Alternate angles) \[\angle \,b={{100}^{\text{o}}}\] \[m\angle a+m\angle b={{70}^{\text{o}}}+{{100}^{\text{o}}}={{170}^{\text{o}}}\]