anonymous
  • anonymous
Kite DCFE is inscribed in circle A shown below. If the measure of is 232°, what is the measure of ∠ DEF? (5 points)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
mathstudent55
  • mathstudent55
The measure of what is 232 deg? The info is missing in your post.
anonymous
  • anonymous
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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anonymous
  • anonymous
Oh oops hold on
anonymous
  • anonymous
The measure of DEF @mathstudent55
mathstudent55
  • mathstudent55
Angle DEF?
anonymous
  • anonymous
Yes.
mathstudent55
  • mathstudent55
Arc DEF?
anonymous
  • anonymous
No angle DEF
mathstudent55
  • mathstudent55
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?
mathstudent55
  • mathstudent55
|dw:1434041246519:dw|
anonymous
  • anonymous
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.
mathstudent55
  • mathstudent55
|dw:1434041331681:dw|
anonymous
  • anonymous
Naw, its the other way from DE. Sorry for the confusion
mathstudent55
  • mathstudent55
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?
anonymous
  • anonymous
Yes, sorry
anonymous
  • anonymous
@mathstudent55 Yes, arc DEF
mathstudent55
  • mathstudent55
Ok. Remember a kite is symmetric, so these arcs are congruent. See pic below. |dw:1434041802642:dw|
mathstudent55
  • mathstudent55
If arc DEF measures 232, arcs DE and FE measure half that much.
anonymous
  • anonymous
Why's that?
mathstudent55
  • mathstudent55
Also, because of symmetry of a kite, the angles below are congruent. |dw:1434041934430:dw|
anonymous
  • anonymous
Ahhhh I see
anonymous
  • anonymous
Okay
mathstudent55
  • mathstudent55
Arc measures below: |dw:1434042008754:dw|
mathstudent55
  • mathstudent55
Angle DEF measures twice angle DEC. An inscribed angle measure half of its tended arc.
anonymous
  • anonymous
Wow
anonymous
  • anonymous
But wait
anonymous
  • anonymous
64+64+112 = 244
anonymous
  • anonymous
not 232
mathstudent55
  • mathstudent55
OK. Now that I know what the 232 deg refers to, let's start from the beginning.
mathstudent55
  • mathstudent55
You start like this. |dw:1434042759323:dw|
mathstudent55
  • mathstudent55
You were correct to subtract 232 from 360. You get this: |dw:1434042831738:dw|
mathstudent55
  • mathstudent55
|dw:1434042874732:dw|
mathstudent55
  • mathstudent55
Angle DEF is the inscribed angle of an arc of measure 128, so angle DEF measures half of 128, which is 64.
anonymous
  • anonymous
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
anonymous
  • anonymous
xD
anonymous
  • anonymous
@mathstudent55 Thanks, you get a medal :) well-deserved
mathstudent55
  • mathstudent55
You're welcome.

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