Answer:
[tex]m\angle MON=15^o[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
[tex]m\angle LON=m\angle LOM+m\angle MON[/tex] ---> by addition angle postulate
substitute the given values
[tex]77^o=(9x+44)^o+(6x+3)^o[/tex]
solve for x
[tex]77=(15x+47)[/tex]
[tex]15x=77-47[/tex]
[tex]15x=30\\x=2[/tex]
Find the measure of angle MON
[tex]m\angle MON=(6x+3)^o[/tex]
substitute the value of x
[tex]m\angle MON=(6(2)+3)=15^o[/tex]
