From the circumcentre L of $\triangle \mathrm{XYZ}$, perpendicular LM is drawn on side YZ. If $\angle \mathrm{YXZ}=60^{\circ}$, then the measure of $\angle \mathrm{YLM}$ is:
Answer & explanation
Correct answer: option 1
As L is the circumstance so, \(\angle\)YLZ = 2 \(\angle\)YXZ
So, \(\angle\)YLZ = \({120}^\circ\)
Now,
YL = LZ = radius of the circumcircle
So,
\(\angle\)LYZ = \(\angle\)LZY = \({30}^\circ\)
\(\angle\)YLM = \({180}^\circ\) - \({90}^\circ\) - \({30}^\circ\)
⇒ \({60}^\circ\)
Therefore, \(\angle\)YLM is \({60}^\circ\)