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The image shows a quadrilateral inscribed in a circle. 12 11 10 9 8 7 6 5 4 3 2 1 0 2 3 4 -7 -10 -11 -12 -12-11-10 9 8 7 012 3 4 5 6 7 8 9 10 11 12 hat is the value of x ? A 23.1 B 21.1 C 25.1 D 22.6 E 19.1

The image shows a quadrilateral inscribed in a circle 12 11 10 9 8 7 6 5 4 3 2 1 0 2 3 4 7 10 11 12 121110 9 8 7 012 3 4 5 6 7 8 9 10 11 12 hat is the value of class=


Answer :

We have a quadrilateral inscribed in a circle.

The quadrilateral is a trapezoid.

When we have a quadrilateral inscribed in a circle, opposite angles are supplementary.

Then, we can write:

[tex]\begin{gathered} m\angle C+m\angle B=180\degree \\ 4x+(4x+11)=180 \\ 8x=180-11 \\ 8x=169 \\ x=\frac{169}{8} \\ x=21.125 \\ x\approx21.1 \end{gathered}[/tex]

Answer: x = 21.1

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