Answer:
m∠LMN=\(90\°\)
Step-by-step explanation:
we know that
The measurement of the external angle is the semi-difference of the arcs which comprises
In this problem
m∠LMN ---> is the external angle
m∠LMN=\(\frac{1}{2}[major\ arc\ LN- minor\ arc\ LN]\)
we have that
\(major\ arc\ LN=270\°\)
\(minor\ arc\ LN=360\°-270\°=90\°\)
substitute
m∠LMN=\(\frac{1}{2}[270\°- 90\°]\)
m∠LMN=\(\frac{1}{2}[180\°]\)
m∠LMN=\(90\°\)
