Answer:
FGE = 44 degrees
CD = 72 degrees
Step-by-step explanation:
Let's solve for FGE first;
We know that CGD and FGE are verticals angles and therefore congruent, so if;
CGD = FGE
44 = FGE
Now let's solve for CD;
- We know that arc FED is 180 since the central angle it intersects is a semicircle.
- We also know that arc ED is congruent to arc FC.
- We also know that measure of arc FBE is 72.
Therefore we can say;
FED = FBE + ED
180 = 72 + ED
180 - 72 = ED
108 = ED
So;
FC also = 108
Now we know that the measure of a whole circle is 360 and here we are given 4 arcs that make up a full circle;
FBE + ED + DC + CF = 360
72 + 108 + DC + 108 = 360
288 + DC = 360
DC = 360 - 288
DC = 72
Hope this helps!
