Answer:
The measure of angle N is equal to [tex]27\°[/tex]
Step-by-step explanation:
we know that
The triangle LMO is an isosceles triangle
therefore
[tex]LO=MO[/tex]
and
[tex]m<OLM=m<LMO[/tex]
see the attached figure to better understand the problem
we have that
[tex]m<OLM=55\°[/tex]
so
[tex]m<LMO=55\°[/tex]
Remember that
[tex]m<LMO+m<OMN=180\°[/tex] -----> by supplementary angles
Find the measure of angle OMN
[tex]55\°+m<OMN=180\°[/tex]
[tex]m<OMN=180\°-55\°=125\°[/tex]
The sum of the internal angles of a triangle is equal to [tex]180\°[/tex]
In the triangle OMN
[tex]m<MON+m<OMN+m<MNO=180\°[/tex]
we have
[tex]m<OMN=125\°[/tex]
[tex]m<MON=28\°[/tex]
substitute and solve for m< NMO
[tex]28\°+125\°+m<MNO=180\°[/tex]
[tex]m<MNO=180\°-28\°-125\°=27\°[/tex]
