Answer:
[tex]m\angle EFG=52^{o}[/tex]
Step-by-step explanation:
We have been given that line m is parallel to line p, [tex]m\angle HEF=39^{o}[/tex] and [tex]m\angle IGF=13^{o}[/tex].
Since line m is parallel to line p and EJ is a transversal, so measure of angle EJG will be 39 degrees as angle EJG is alternate interior angle of angle HEF. Both angles are inside parallel lines m and p and on opposite side of transversal EJ.
We can see that angle EFG is exterior angle of triangle GFJ. Since the measure of an exterior angle of a triangle equals to the sum of the opposite interior angles.
We can see that angle IGF and angle EJG are opposite interior angles of angle EFG.
[tex]m\angle EFG=m\angle IGF+m\angle EJG[/tex]
Upon substituting our given values we will get,
[tex]m\angle EFG=13^{o}+39^{o}[/tex]
[tex]m\angle EFG=52^{o}[/tex]
Therefore, measure of angle EFG is 52 degrees.