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ABCD is a cyclic quadrilateral. Angle A, Angle B and Angle C form an arithmetic sequence in this order. What is Angle D in degrees?
 

I was pretty stuck on this question. Thanks!

 Feb 23, 2020
 #1
avatar+109450 
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Let  A  =  A

Let B =  A + d

Let C  = A  + 2d

 

 

Note that    A  +  C  will be supplementary......so....

 

A + (A + 2d)  = 180

 

2A  +  2d  = 180         divide through by  2  

 

A  +  d    =   90

 

And     B   + D   are also supplementary

 

So

 

(A + d )  +  D  =   180

 

90  + D   =  180     subtract  90  from both sides

 

D  =  90°

 

Note  that  B  must also   = 90°

 

And   A , B , C   are in arithmetic progression  if  A  = 60°  and  C  =120°

 

 

cool cool cool

 Feb 23, 2020

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