Define a cyclic quadrilateral by a quadrilateral that is circumscribed by a circle. In this case, since the quadrilateral shown is circumscribed by a circle, it is a cyclic quadrilateral.

A property of all cyclic quadrilaterals is that their opposite angles are supplementary, meaning they add up to 180 degrees. Since $\angle G$ and $\angle I$ are opposite angles in the quadrilateral, they must be supplementary. Therefore, we have the equation:

$\angle G+\angle I=180,\\81^{\circ}+\angle I=180,\\\angle I=180-81=\boxed{99^{\circ}}$

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What is the measure of one interior angle of a regular polygon that has 40 sides?

s344n2d4d5 [400]

Hope this is correct and hope it helps x

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