If \[\angle B={{70}^{o}}\] and\[\angle C={{35}^{o}}\], find\[\angle MAN\].
A) \[{{17.5}^{o}}\]
B) \[{{27.5}^{o}}\]
C) \[{{37.5}^{o}}\]
D) \[{{47.5}^{o}}\]
Correct Answer: A
Solution :
\[\angle NAB=\angle NAC=\frac{1}{2}\angle A\] In \[\Delta ABC,\,\angle A={{75}^{o}}\therefore \frac{1}{2}\angle A={{37.5}^{o}}\] From \[\Delta ABN,\angle BAM={{20}^{o}}.\] \[\therefore \]\[\angle MAN={{37.5}^{o}}-{{20}^{o}}={{17.5}^{o}}.\]
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