Question

Na figura abaixo, OP é bissetriz do ângulo AOB. Determine o valor de x e y
a) x = 13 e y = 49
b) x = 15 e y = 35
c) x = 12 e y = 48
d) x = 17 e y = 42
e) x = 10 e y = 50

Answer 1

$\sf y-10^\circ=x+30^\circ\\\sf y-x=30^\circ+10^\circ\\\sf y-x=40^\circ\\\sf 2y+y-10^\circ+x+30^\circ=180^\circ\\\sf 3y+x=180^\circ+10^\circ-30^\circ\\\sf 3y+x=160^\circ$

$+\underline{\begin{cases}\sf y-\diagup\!\!\!\!x=40^\circ\\\sf3y+\diagup\!\!\!\!x=160^\circ\end{cases}}\\\sf4y=200^\circ\\\sf y=\dfrac{200^\circ}{4} \\\sf y=50^\circ\checkmark\\\sf y-x=40^\circ\\\sf x=y-40^\circ\\\sf x=50^\circ-40^\circ\\\sf x=10^\circ\checkmark$