Question

determine o valor de A e B​

Answer 1

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$\boxed{\begin{array}{l}\sf3\alpha+\beta+48^\circ=90^\circ\\\sf 3\alpha+\beta=90^\circ-48^\circ\\\sf 3\alpha+\beta=42^\circ\\\sf 5\beta+2\alpha+10^\circ=90^\circ\\\sf 5\beta+2\alpha=90^\circ-10^\circ\\\sf 5\beta+2\alpha=80^\circ\end{array}}$

$\boxed{\begin{array}{l}\begin{cases}\sf3\alpha+\beta=42^\circ\\\sf2\alpha+5\beta=80^\circ\end{cases}\\\begin{cases}\sf\beta=42^\circ-3\alpha\\\sf 2\alpha+5\beta=80^\circ\end{cases}\\\sf 2\alpha+5\cdot(42^\circ-3\alpha)=80^\circ\\\sf 2\alpha+210^\circ-15\alpha=80^\circ\\\sf 15\alpha-2\alpha=210^\circ-80^\circ\\\sf 13\alpha=130^\circ\\\sf\alpha=\dfrac{130^\circ}{13}\\\sf\alpha=10^\circ\\\sf \beta=42^\circ-3\alpha\\\sf\beta=42^\circ-3\cdot10^\circ\\\sf\beta=42^\circ-30^\circ\\\sf\beta=12^\circ\end{array}}$