Answer:
Explanation:
Opposite angles in a cyclic quadrilateral are supplementary.
Application
x° = 180° -105°
x° = 75°
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The value of the other angle is similarly found:
w° = 180° -80°
w° = 100°
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Additional comment
This result comes from the inscribed angle theorem. That theorem tells you the measure of the inscribed angle is half the measure of the intercepted arc.
The opposite angles of a cyclic quadrilateral intercept the circle at the same two points, dividing the total 360° circle into two parts. Each angle has a measure equal to half its corresponding arc, so the total of the two angles is half the total of the two arcs: 360°/2 = 180°. The angles are supplementary.