Kite DCFE is inscribed in circle A shown below.

If the measure of is 232°, what is the measure of ∡DEF?

Question

Kite DCFE is inscribed in circle A shown below. 

 

If the measure of  is 232°, what is the measure of ∡DEF?

anonymous · Answer

attachment

jim_thompson5910 · Answer

It says "If the measure of is 232°, ", but the part before the "is 232" is missing. Which angle is it?

anonymous · Answer

This is what it has on it

jim_thompson5910 · Answer

Oh ok, thx

Arc DEF = 232

So arc DCF = 360 - 232 = 128

By the inscribed angle theorem, angle DEF = (1/2)*arc DCF = (1/2)*(128) = 64


So the answer is 64 degrees

anonymous · Answer

Can you kind of go over how you got that? I don't fully understand

jim_thompson5910 · Answer

arc DEF and arc DCF fully form a circle. So the arc measures must add to 360 degrees. 

This means that 

arc DEF + arc DCF = 360


Solve for arc DCF to get


arc DCF = 360 - arc DEF


From there, I plugged in arc DEF = 232 and I computed arc DCF

jim_thompson5910 · Answer

Once I figured out the measure of arc DCF, I used the inscribed angle theorem to find angle DEF

anonymous · Answer

Ok, that makes sense. Thanks!

jim_thompson5910 · Answer

you're welcome