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

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1 Answer
May 12, 2017

Answer:

#mangleA=77^@#

Explanation:

Consider the property of cyclic quadrilaterals for which opposite angles are supplementary, then:
#mangleA+mangleC=180^@#

Since we are given that #mangleA=(2x+9)^@# and #mangleC=(3x+1)^@#, we can substitute to find the value of #x#:
#2x+9+3x+1=180#
#5x+10=180#
#5x=170#
#x=34#

Now, we can substitute in the above value of #x# to find #mangleA#:
#mangleA=(2x+9)^@=(2*34+9)^@=77^@#

Therefore, the #mangleA=77^@#