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Arisa [49]
2 years ago
15

If FBE=72 what is fge and cd?

Mathematics
1 answer:
ikadub [295]2 years ago
7 0

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

<u><em>44 = FGE</em></u>

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

<em><u>DC = 72</u></em>

Hope this helps!

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