Answer:
[tex]m\angle LKM=36^o[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Find the measure of arc KN
we know that
The inscribed angle is half that of the arc comprising
so
[tex]m\angle M=\frac{1}{2}(arc\ KN)[/tex]
we have
[tex]m\angle M=48^o[/tex]
substitute
[tex]48^o=\frac{1}{2}(arc\ KN)[/tex]
[tex]arc\ KN=96^o[/tex]
step 2
Find the measure of arc LM
we know that
[tex]arc\ KN=arc\ MN=arc\ KL=96^o[/tex]
so
[tex]3arc\ KN+arc\ LM=360^o[/tex] ----> by complete circle
substitute given value
[tex]3(96^o)+arc\ LM=360^o[/tex]
[tex]arc\ LM=360^o-288^o=72^o[/tex]
step 3
Find the measure of angle LKM
we know that
The inscribed angle is half that of the arc comprising
so
[tex]m\angle LKM=\frac{1}{2}(arc\ LM)[/tex]
substitute the given value
[tex]m\angle LKM=\frac{1}{2}(72^o)=36^o[/tex]
