Question

find ( mangle g ).

( mangle g = square^circ )

Explanation:

Step1: Calculate remaining arc measure

The total circumference of a circle is $360^\circ$. Subtract the given arcs:
$m\overset{\frown}{FD} = 360^\circ - 70^\circ - 120^\circ = 170^\circ$

Step2: Apply inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. $\angle G$ intercepts $\overset{\frown}{FD}$:
$m\angle G = \frac{1}{2} \times m\overset{\frown}{FD}$
$m\angle G = \frac{1}{2} \times 170^\circ$

Answer:

$85^\circ$