Question

Num quadrilátero convexo ABCD os ângulos internos são expressos por:
 = 2x + 10°
B= 7x - 10°
C= x + 30°,
D= 8x - 300
Qual o valor de cada ângulo?​

Answer 1

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$\rm{a~soma~dos~\hat{a}ngulos~de~um~quadril\acute{a}tero~\acute{e}~360^{\circ}}\\\sf{2x+\diagdown\!\1\!\!\!10^{\circ}+7x-\diagdown\!\!\!\!\!\!10^{\circ}+x+30^{\circ}+8x-300^{\circ}=360^{\circ}}\\\sf{18x=360^{\circ}+270^{\circ}}\\\sf{x=\dfrac{630^{\circ}}{18}=\dfrac{7\cdot\diagdown\!\!\!\!9\cdot10^{\circ}}{2\cdot\diagdown\!\!\!\!9}}\\\sf{x=\dfrac{7\cdot\diagup\!\!\!\!\!\!10^{\circ}}{\diagup\!\!\!\!\!2}}\\\sf{x=35^{\circ}}$

$\huge\boxed{\boxed{\boxed{\boxed{\tt{\hat{A}=80^{\circ}}}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\tt{\hat{B}=235^{\circ}}}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\tt{\hat{C}=65^{\circ}}}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\tt{\hat{D}=-20^{\circ}}}}}}$