Answer:
[tex]{\angle}LMO=47.5^{\circ}[/tex]
Step-by-step explanation:
We know that the circumscribed angle is the half of the difference of the major arc and the minor arc, that is
[tex]CA=\frac{1}{2}(major arc- minor arc)[/tex]
Substituting the values from the figure given, we get
[tex]{\angle}LMO=\frac{1}{2}(arcLO-arcLN)[/tex]
[tex]{\angle}LMO=\frac{1}{2}(155^{\circ}-60^{\circ})[/tex]
[tex]{\angle}LMO=\frac{1}{2}(95^{\circ})[/tex]
[tex]{\angle}LMO=47.5^{\circ}[/tex]
Thus, the measure of [tex]{\angle}LMO[/tex] is [tex]47.5^{\circ}[/tex].
