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DiKsa [7]
2 years ago
11

Quadrilateral ABCD​ is inscribed in this circle.

Mathematics
1 answer:
Svetllana [295]2 years ago
5 0

Answer:

132°

Step-by-step explanation:

Quadrilateral ABCD is inscribed in a circle,

So, it is a cyclic quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

\implies \: x \degree + (3x - 12) \degree = 180 \degree \\  \\ \implies \: (4x - 12) \degree = 180 \degree \\  \\  \implies \: 4x - 12  = 180  \\  \\ \implies \: 4x   = 180  + 12 \\  \\ \implies \: 4x   = 192 \\  \\ \implies \: x   =  \frac{192}{4}  \\  \\ \implies \: x   = 48\\\\

(3x-12)° = (3*48 - 12)° = (144 - 12)° = 132°

\implies \: m\angle B   = 132\degree\\\\

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