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I don't think that I am setting the last one up correctly. Each time I try solving it, I get a negative answer. The others I'm confused on. Please help. Thanks!

 Oct 1, 2019
 #1
avatar+19832 
+1

The last one:   the two angles encompass the entire circle 3600

    remember, inscribed angles in a circle intercept arcs TWICE their measure

 

 

2 * (2x  + 4x+24)  = 360

x = 26

sooo     EFC =4x +24 = 4*26   + 24 =    128 degrees

 Oct 1, 2019
 #2
avatar+104911 
+1

First one

Central angles EAJ and EKJ span the same arcs as their measure

So....angle EKJ will span  an arc of  360 - 168  =  192°

 

Second one

This one is similar to the first

Since arc QRT  =198°

Then arc QAT   = angle QAT  =  360 - 198  = 162°  

 

Last one

Quadrilateral DEFC  is a cyclic quadrilateral.....opposite angles will sum to 180°

So...The sum of angles  EDC and EFC  = 180°

So

2x  +  (4x + 24)  = 180

6x + 24  = 180       subtract 24 from both sides

6x  = 156   divide both sides by 6

x = 26

So...angle EFC  = (4(26) + 24)  =   128°

 Oct 1, 2019
edited by CPhill  Oct 1, 2019
 #3
avatar+305 
+2

angle EKJ will span  an arc of  360 - 168  =192

 

angle EFC  = (4(26) + 24)  =   128°

 Oct 1, 2019

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