Answer
$negative$, $II$, $45^\circ$, $-\sqrt 2$.
Work Step by Step
We can identify $\theta=135^\circ$ to be in quadrant $II$, thus $sec\theta=\frac{1}{cos\theta}$ will be $negative$. The reference angle is the acute angle formed by the terminal line with x-axis and it can be found as $180^\circ-135^\circ=45^\circ$, thus the exact value is $sec\theta=-\frac{1}{cos45^\circ}=-\sqrt 2$.
The answers are $negative$, $II$, $45^\circ$, $-\sqrt 2$.
