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

This Question is Closed

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The measure of what is 232 deg? The info is missing in your post.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The measure of DEF @mathstudent55

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Wait. 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
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434041246519:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The 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
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434041331681:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Naw, its the other way from DE. Sorry for the confusion

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Arc 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
 one year ago
Best ResponseYou've already chosen the best response.0@mathstudent55 Yes, arc DEF

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Ok. Remember a kite is symmetric, so these arcs are congruent. See pic below. dw:1434041802642:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1If arc DEF measures 232, arcs DE and FE measure half that much.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Also, because of symmetry of a kite, the angles below are congruent. dw:1434041934430:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Arc measures below: dw:1434042008754:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Angle DEF measures twice angle DEC. An inscribed angle measure half of its tended arc.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1OK. Now that I know what the 232 deg refers to, let's start from the beginning.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You start like this. dw:1434042759323:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You were correct to subtract 232 from 360. You get this: dw:1434042831738:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434042874732:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Angle DEF is the inscribed angle of an arc of measure 128, so angle DEF measures half of 128, which is 64.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OH 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
 one year ago
Best ResponseYou've already chosen the best response.0@mathstudent55 Thanks, you get a medal :) welldeserved
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