Answer:
[tex]296^{\circ}[/tex]
Step-by-step explanation:
It is given that figure shows circle C with diameter LM and inscribed ∠LMN and m∠LMN=32°
.
We know that the angle formed at the center is double the angle formed on the vertex that is an inscribed angle, thus on joining NC, we have
[tex]{\angle}NCL=2({\angle}LMN)[/tex]
Substituting the given values, we have
[tex]{\angle}NCL=2(32^{\circ})[/tex]
[tex]{\angle}NCL=64^{\circ}[/tex]
Now, [tex]minor{\angle}LCN+major{\angle}LCN=360^{\circ}[/tex] (complete angle)
[tex]major{\angle}LCN=296^{\circ}[/tex]
Therefore, the measure of the arc LMN is [tex]296^{\circ}[/tex].
