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The measure of what is 232 deg? The info is missing in your post.

Oh oops hold on

The measure of DEF @mathstudent55

Angle DEF?

Yes.

Arc DEF?

No angle DEF

|dw:1434041246519:dw|

|dw:1434041331681:dw|

Naw, its the other way from DE. Sorry for the confusion

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|

xD

@mathstudent55 Thanks, you get a medal :) well-deserved

You're welcome.