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:

60°

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 \({60}^\circ\)