What is the measure of\[\angle p\]?
A) \[{{53}^{o}}\]
B) \[{{148}^{o}}\]
C) \[{{159}^{o}}\]
D) \[{{212}^{o}}\]
Correct Answer: C
Solution :
\[\angle p+\angle q+{{58}^{o}}+{{90}^{o}}={{360}^{o}}\] \[3\angle q+\angle q+{{148}^{o}}={{360}^{o}}\] \[4\angle q={{360}^{o}}-{{148}^{o}}={{212}^{o}}\] \[\therefore \] \[\angle q=\frac{{{212}^{o}}}{4}={{53}^{o}}\] \[\angle p=3\angle q=3\times {{53}^{o}}={{159}^{o}}\]
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