In the diagram below, \(\mathrm{O}\) is the center of the circle through points \(\mathrm{LM}\) and \(\mathrm{N}\). If \(<\mathrm{MLN}=74^{\circ}\) and \(\angle \mathrm{MNL}=39^{\circ}\). Calculate \(\angle \mathrm{LON}\)
A. \(134^{\circ}\) B. \(67^{\circ}\) C. \(100^{\circ}\) D. \(126^{\circ}\)
Correct Answer: A
Explanation
\(74^{\circ}+39^{\circ}+\mathrm{LMN}=180^{\circ}\) (sum of \(\angle \mathrm{s}\) in a \(\left.\triangle\right)\) \(113^{\circ}+\mathrm{LM} N=180^{\circ}\), \(\mathrm{LMN}=180^{\circ}-113^{\circ}=67^{\circ}\) LÔN \(=2 \times \mathrm{LMN}\) ( \(\angle\) at the centre) \(=2 \times 67^{\circ}=134^{\circ}\)
