we know that
An isosceles triangle has two equals sides and two equals angles
so
EF=GF
m∠EGF=m∠GEF
The sum of the internal angles of a triangle must be [tex]180[/tex] degrees
m∠EGF+m∠GEF+m∠EFG=[tex]180\°[/tex]
we have
m∠EFG=[tex]50\°[/tex]
2m∠EGF+[tex]50\°=180\°[/tex]
2m∠EGF=[tex]180\°-50\°[/tex]
2m∠EGF=[tex]130\°[/tex]
m∠EGF=[tex]65\°[/tex]
therefore
the answer Part a) is
the measure of angle EGF is [tex]65\°[/tex]
Part b) What is the measure of m∠CGF?
we know that
m∠CGF+m∠EGF=[tex]180\°[/tex] ---------> by supplementary angles
substitute values
m∠CGF+[tex]65\°=180\°[/tex]
m∠CGF=[tex]180\°-65\°[/tex]
m∠CGF=[tex]115\°[/tex]
therefore
the answer Part b) is
the measure of angle CGF is [tex]115\°[/tex]
