Question

In figure, $O$ is centre of circle. The measure of $\angle LMN$ is ${110}^o$. Find the measure of $\angle ONL$

Answer 1

From the inscribed angle theorem, $\angle LON={360}^{\circ }-2\theta ={360}^{\circ }-{220}^{\circ }={140}^{\circ }$

$\Delta LON$ is isosceles, since $OL=ON$ $\Rightarrow =\angle OLN=\angle ONL$

$2\angle ONL+{140}^{\circ }={180}^{\circ }$

$\Rightarrow \angle ONL={20}^{\circ }$