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Quadrilateral ABCD is inscribed in a circle.
What is the measure of angle A?

Enter your answer in the box.

m∠A= [ ]°

flanspawn  May 11, 2018
 #1
avatar+2202 
+1

The figure ABCD has four sides, and its vertices lie on a circle. This situation has a specific name: cyclic quadrilateral. This situation also has a specific theorem associated to it: Opposite angles of a cyclic quadrilateral are supplementary. Let's use this theorem to our advantage:

 

\(m\angle A+m\angle C=180^{\circ}\) Substitute in the known expressions for both of these angles. 
\(3x+6+x+2=180\) Now, simplify the left-hand side as much as possible.
\(4x+8=180\) Now, use algebraic manipulation to isolate the variable. 
\(4x=172\)  
\(x=43\) Now, find the measure of the missing angle.
\(m\angle A=3x+6\) Substitute in the known value for x. 
\(m\angle A=3*43+6\) Simplify.
\(m\angle A=135^{\circ}\)  


 

TheXSquaredFactor  May 11, 2018

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