Answer:
m∠LMN=[tex]90\°[/tex]
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=[tex]\frac{1}{2}[major\ arc\ LN- minor\ arc\ LN][/tex]
we have that
[tex]major\ arc\ LN=270\°[/tex]
[tex]minor\ arc\ LN=360\°-270\°=90\°[/tex]
substitute
m∠LMN=[tex]\frac{1}{2}[270\°- 90\°][/tex]
m∠LMN=[tex]\frac{1}{2}[180\°][/tex]
m∠LMN=[tex]90\°[/tex]
