Answer:
[tex]m\angle LMN=90^{O}[/tex]
Step-by-step explanation:
We know that the outside angle formed between two tangents of a circle can be found by taking half of difference of bigger arc angle and smaller arc angle.
We can express it as:
[tex]m\angle LMN=\frac{m\widehat{LN}_{Bigger}-m\widehat{LN}_{Smaller}}{2}[/tex]
From the given diagram, we get:
[tex]m\widehat{LN}_{Bigger}=270\\m\widehat{LN}_{Smaller}=360-270=90[/tex]
Upon substituting these values in the formula, we get:
[tex]m\angle LMN=\frac{270-90}{2}=\frac{180}{2}=90\\m\angle LMN=90^{0}[/tex]
