Question

A metade da medida de um ângulo menos a quinta parte de seu complemento mede 38° . Qual a medida desse ângulo ??

Answer 1

Considerando o angulo desconhecido como sendo β, lembrando que o complemento de um angulo significa o quanto falta para completar 90º. Logo:

$\mathsf{\dfrac{\beta }{2}-\dfrac{90-\beta }{5}=38}\\\\\\\mathsf{\dfrac{5\cdot \beta }{5\cdot 2}-\dfrac{2\cdot \left(90-\beta \right)}{2\cdot 5}=38}\\\\\\\mathsf{\dfrac{5\beta }{10}-\dfrac{180-2\beta }{10}=38}\\\\\\\mathsf{\dfrac{5\beta -180+2\beta }{10}=38}\\\\\\\mathsf{5\beta -180+2\beta =380}\\\\\\\mathsf{7\beta -180=380}\\\\\\\mathsf{7\beta =380+180}\\\\\\\mathsf{7\beta =560}\\\\\\\mathsf{\beta =\dfrac{560}{7}}\\\\\\\boxed{\mathsf{\beta =80^{\circ }}}\: \: \checkmark$