Question 860018: A quadrilateral (Not Regular) is inscribed in a circle. One of the angles is 82°, find the angle that is opposite the given angle. need the answer and calculations to get the answer.
Answer by ben720(159)   (Show Source):
You can put this solution on YOUR website! The opposite angle is 98° by the Opposite Angles of Cyclic Quadrilaterals Conjecture.
If you don't know what the Opposite Angles of Cyclic Quadrilaterals Conjecture is, it is that the opposite angles of cyclic quadrilaterals are supplementary.
To prove this, take a circle. The two opposite angles in the quadrilateral are the inscribed angles of two arcs. Those arcs comprise the entire circle.
Therefore, as the measure of an inscribed angle is half that of the arc it defines, the two angles add up to 180°.
This conjecture has a weird proof; if you would like to have more clarification, feel free to email be at benfasigal AT gmail DOT com
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