Answer:
108°
Step-by-step explanation:
CB and CA are tangents to the circle at points E and F respectively. GE and GF are radii of the circle with center G.
Since, radii of a circle are perpendicular to the tangents at the point of contacts.
[tex] \therefore GE \perp CB\\\\
\& \:GF \perp CA\\\\
m\angle GEC =m\angle GFC = 90\degree \\\\[/tex]
In quadrilateral GECF, by interior angle sum property:
[tex] m\angle C + m\angle E + m\angle F + m\angle EGF = 360\degree \\\\
\therefore 72\degree + 90\degree + 90\degree + m\angle EGF = 360\degree \\\\
\therefore 252\degree + m\angle EGF = 360\degree \\\\
\therefore m\angle EGF = 360\degree - 252\degree \\\\
\therefore m\angle EGF = 108\degree \\[/tex]
