Answer
$R = 240~\Omega$
Work Step by Step
We can find the value of $R$:
$\frac{1}{75~\Omega} = \frac{1}{200~\Omega}+\frac{1}{R}+\frac{1}{R}$
$\frac{1}{75~\Omega} - \frac{1}{200~\Omega} = \frac{1}{R}+\frac{1}{R}$
$\frac{8}{600~\Omega} - \frac{3}{600~\Omega} = \frac{2}{R}$
$\frac{5}{600~\Omega} = \frac{2}{R}$
$\frac{R}{2} = \frac{600~\Omega}{5}$
$R = 240~\Omega$
