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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?

 Feb 26, 2019

Best Answer 

 #1
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\(\text{an arithmetic sequence is }a, a+r, a+2r, \dots, a+k r, \dots\\ s_n = a + (n-1)r\\ \text{The angles of a quadrilateral sum to 360 degrees}\\ \text{The angles of a cycle quadrilateral sum to 180 degrees}\\ a + (a+r) + (a+2r) = 360-D\\ 3a+3r = 360-D\\ a + (a+2r) = 180\\ 2a+2r=180\\ 3a+2r = 270\\ D=360-270=90\)

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 Feb 26, 2019
 #1
avatar+4423 
+2
Best Answer

\(\text{an arithmetic sequence is }a, a+r, a+2r, \dots, a+k r, \dots\\ s_n = a + (n-1)r\\ \text{The angles of a quadrilateral sum to 360 degrees}\\ \text{The angles of a cycle quadrilateral sum to 180 degrees}\\ a + (a+r) + (a+2r) = 360-D\\ 3a+3r = 360-D\\ a + (a+2r) = 180\\ 2a+2r=180\\ 3a+2r = 270\\ D=360-270=90\)

Rom Feb 26, 2019
 #2
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THANK YOU SOOO MUCH!

 Feb 27, 2019

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