The bearing of P and Q from a common point N are 020o and 300o respectively. If P and Q are also equidistance from N, find the bearing of P from Q
040o
070o
280o
320o
$\begin{align} & \angle QNP={{80}^{o}} \\ & \text{Since }P\text{ and }Q\text{ are equidistant from }N \\ & \left| NQ \right|=\left| NP \right| \\ & \angle NQP=\angle NPQ\text{ }\!\!\{\!\!\text{ Base angle of an issosceles triangle }\!\!\}\!\!\text{ } \\ & \text{8}{{\text{0}}^{o}}+x+x=180\text{ }\!\!\{\!\!\text{ sum of angle in }\Delta QNP\text{ }\!\!\}\!\!\text{ } \\ & 2x={{100}^{o}} \\ & x={{50}^{o}} \\ & \angle NQP=\angle NPQ=x={{50}^{o}} \\ & \angle NTQ=\angle NOQ={{60}^{o}}\text{ }\!\!\{\!\!\text{ alternate angles }\!\!\}\!\!\text{ } \\ & \text{The bearing of }P\text{ from }Q={{180}^{o}}-({{50}^{o}}+{{60}^{o}})={{070}^{\circ }}\text{ } \\ & \text{ }\!\!\{\!\!\text{ sum of angles on straight line }\!\!\}\!\!\text{ } \\\end{align}$