Quadrilateral ABCD is inscribed in this circle.

1 answer:

3 0

When the quadrilateral is inscribed in a circle (a "cyclic" quadrilateral), opposite angles are supplementary. This fact gives a relationship between angles B and D that lets us find the value of x.
∠B + ∠D = 180
(2x-4) + (3x+9) = 180
5x +5 = 180
x = (180 -5)/5 = 35

Now, we can find angle C as
∠C = 180 - ∠A
∠C = 180 - (2×35+3)
∠C = 107°

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​ Quadrilateral ABCD ​ is inscribed in this circle.

Quadrilateral ABCD is inscribed in this circle.