Question

If FBE=72 what is fge and cd?

Answer 1

FGE = 44 degrees

CD = 72 degrees

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!