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I am having such a difficult time with these questions. I think arc mDE is 104 and arc mFE is 76 but I don't think the answers are correct. Please help. I'm very sorry. Please show work so maybe I can understand it.

 Sep 9, 2019
 #1
avatar+104723 
+1

First one....you are correct  !!!

 

So arc DEF  =   104 + 76  =  180°

 

Note that arc CF  = arc DE....so.....

 arc  CFD  = 104 + 180  =  284°

 

 

And arc DFE  =  arc DCF + arc FE   =180 +   76  =    256°

 

 

 

cool cool cool

 Sep 9, 2019
 #2
avatar+104723 
+1

Second one ....top right

 

Note that arc QU  = arc RS  = 25°

 

arc TQ  =  arc TU + arc QU  =  44 + 25   =   69° 

 

To find arc QR, we need to do a little work

 

arc QS  = 180

arc RS  =  25

So   arc QR   =      arc QS - arc RS  =   180 - 25  =  155°

 

 

arc TS  =   arc QR  - arc UT  - arc  RS  =   180 -  44 - 25  =  180 - 69  = 111°

 

 

arc SQR  =    arc SQ + arc  arc QR   =  180 + 165  =   345°

 

arc RQT   = arc RU  + arc UT   =   180 + 44   =  224°

 

 

cool cool cool

 Sep 9, 2019
 #3
avatar+104723 
+1

Third one ......bottom left

 

Note that arc KN  = 180°

And arc NM  = 90°

And arc LM  = 67°

 

So....

 

arc KL  =   180  - 90 - 67  =  90 - 67  =  23°  = arc ON

 

arc LON   =  arc LO + arc ON  =  180 + 23   =  203°

 

arc OM  =  arc ON + arc NM  =   23 + 90  =  113° 

 

arc KNL   = 360 - arc KL  =  360  - 23   =  337°

 

arc NL  =  arc NM + arc LM  =  90 + 67  =  157° 

 

 

 

cool cool cool

 Sep 9, 2019
 #4
avatar+104723 
+1

Last one°

 

arc YU  = arc XV - arc XY - arc UV  =   180  - 55 - 108  =  180 - 163  =  17°

 

arc XW  =  arc YW  - arc YX  =  180 - 55   =  125°

 

arc XVW  = arc YW + arc XY =  180 + 55  =  235°

 

arc VW  =  arc XY  =  55°

 

arc YWU  = 360 - arc YU  =  360 - 17  =  343°

 

 

cool cool cool

 Sep 9, 2019

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