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

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Answer 1 · 2018-05-17T07:56:25

$133^{o}$ $133^o$

the quadrilateral is a cyclic quadrilateral, and its fundamental property is that the opposite angles are supplementary

ie they add up to $180^{o}$ $180^o$

$:.4x+5+x+15=180$

$5x+20=180$

$5x=180-20=160$

$x=160/5=32$

$:. < A=4xx32+5=128+5=133$