Kite DCFE is inscribed in circle A shown below. If the measure of is 232°, what is the measure of ∠ DEF? (5 points)

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Kite DCFE is inscribed in circle A shown below. If the measure of is 232°, what is the measure of ∠ DEF? (5 points)

Mathematics
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The measure of what is 232 deg? The info is missing in your post.
I know that a circle = 360 and that 360 - 232 = 128 but 128 is the arc of angle FDE not DEF? I also know that the inscribed angles theorem means that angles = 1/2 the value of their intercepted arcs.

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Oh oops hold on
The measure of DEF @mathstudent55
Angle DEF?
Yes.
Arc DEF?
No angle DEF
Wait. We are looking for the measure of angle DEF. That much I see in your post. What measures 232 deg? Is it arc DEF or something else?
|dw:1434041246519:dw|
The question is this: If the measure of ARC DE is 232°, what is the measure of ∠ DEF? I have shared an imagine. This is as much as I know: I know that a circle = 360 and that 360 - 232 = 128 but 128 is the arc of angle FDE not DEF? I also know that the inscribed angles theorem means that angles = 1/2 the value of their intercepted arcs.
|dw:1434041331681:dw|
Naw, its the other way from DE. Sorry for the confusion
Arc DE cannot be 232 deg because arc FE is congruent to arc FE, and just that would total more than 360 deg. Is it measure of arc DEF that is 232?
Yes, sorry
@mathstudent55 Yes, arc DEF
Ok. Remember a kite is symmetric, so these arcs are congruent. See pic below. |dw:1434041802642:dw|
If arc DEF measures 232, arcs DE and FE measure half that much.
Why's that?
Also, because of symmetry of a kite, the angles below are congruent. |dw:1434041934430:dw|
Ahhhh I see
Okay
Arc measures below: |dw:1434042008754:dw|
Angle DEF measures twice angle DEC. An inscribed angle measure half of its tended arc.
Wow
But wait
64+64+112 = 244
not 232
OK. Now that I know what the 232 deg refers to, let's start from the beginning.
You start like this. |dw:1434042759323:dw|
You were correct to subtract 232 from 360. You get this: |dw:1434042831738:dw|
|dw:1434042874732:dw|
Angle DEF is the inscribed angle of an arc of measure 128, so angle DEF measures half of 128, which is 64.
OH MY GOODNESS! Okay I get everything now, I didnt realize that that was DEF I thought ANGLE DEF was from point D to E to F clockwise I get it now
xD
@mathstudent55 Thanks, you get a medal :) well-deserved
You're welcome.

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