Answer:
The measure of angle LMW is
[tex]m\angle LMW=67\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of arc MW
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m\angle MLK=\frac{1}{2}[arc\ MW+arc\ WK][/tex]
substitute the given values
[tex]65\°=\frac{1}{2}[arc\ MW+68\°]\\ 130\°=[arc\ MW+68\°]\\ arc\ MW=130\°-68\°=62\°[/tex]
step 2
Find the measure of arc LK
we know that
[tex]arc\ LM+arc\ MW+arc\ WK+arc\ LK=360\°[/tex] -----> by complete circle
substitute the given values
[tex]164\°+62\°+68\°+arc\ LK=360\°\\ 294\°+arc\ LK=360\°\\ arc\ LK=360\°-294\°=66\°[/tex]
step 3
Find the measure of angle LMW
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m\angle LMW=\frac{1}{2}[arc\ LK+arc\ WK][/tex]
substitute the given values
[tex]m\angle LMW=\frac{1}{2}[66\°+68\°]=67\°[/tex]
