Question

GEOMETRY. image attached

Answer 1

$\bf \measuredangle DFC=\cfrac{1}{2}(\widehat{BG}+\widehat{CD})\implies \measuredangle DFC=\cfrac{\widehat{BG}+\widehat{CD}}{2}$

you know what the arcCD is, and what the angle DFC is, so
solve for the arcBG