question_answer

In the given figure, what is the measure of q?

A) \[{{48}^{o}}\]                      

B)        \[{{90}^{o}}\]  

C) \[{{42}^{o}}\]                    

D)         \[{{110}^{o}}\]

Correct Answer: A

Solution :

Clearly \[p={{360}^{o}}-{{270}^{o}}={{90}^{o}}\] (Angles at a point) Through C, draw a line Z parallel to AB and DE. \[\therefore \] \[{{42}^{o}}+x={{180}^{o}}\]  and  \[q+y={{180}^{o}}\] \[\Rightarrow \] \[x={{180}^{o}}-{{42}^{o}}={{138}^{o}}\] \[\therefore \]  \[y={{270}^{o}}-{{138}^{o}}={{132}^{o}}\] \[\therefore \] \[q={{180}^{o}}-{{132}^{o}}={{48}^{o}}\]