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

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1 Answer
May 12, 2017

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^@