Question

Given that m angle G- 81", what is m angle I? A)81" B)89 C)91 D)99

Answer 1

The answer to the question is D)99

Answer 2

Answer:

$\text{D) }99^{\circ}$

Step-by-step explanation:

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:

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