Answer
$sec$($\theta$ + 180$^{\circ}$) is positive in the interval (90$^{\circ}$,180$^{\circ}$).
Work Step by Step
$\theta$ is in the interval (90$^{\circ}$,180$^{\circ}$)
Therefore: $\theta$ exists in Quadrant II.
Therefore, $\theta$ + 180$^{\circ} $exists in Quadrant IV.
All trigonometric functions are negative, in Quadrant IV, except for $\sec$ and $\cos$. Therefore $sec$($\theta$ + 180$^{\circ}$) is positive in the interval (90$^{\circ}$,180$^{\circ}$).
