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All vertices of pentagon ABCDE lie on a circle. We know that AB = BC = CD = DE and angle ABC = 128. Find angle ACE in degrees.

 Jan 13, 2019
 #1
avatar+533 
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i dont know how to solve this, but i think a way to make it easier is to draw all the diagonals

 Jan 14, 2019
 #2
avatar+99585 
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Just a rough pic for reference......definitely not exact!!!!

 

                     A

        

     E                            B

 

   

  D

                        C                                     

                           

                                   

Since ABC = 128°.......then major arc CA is twice 128° = 256°

 

Therefore.......arc ABC =  360° - 256° = 104°

 

But.....since AB = BC....then each of these chords must span an arc of 52°

 

And since  AB = BC = CD = DE.....these equal chords each span an arc of 52°

 

So....arc EA  must be   360 - 4(52)  = 152°

 

And angle ACE is an inscrbed angle subtending EA....so it's measure is (1/2) measure arc EA = 76°

 

 

 

cool cool cool

 Jan 14, 2019

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