Answer
$107^{\circ}$
Work Step by Step
Given-
$\sec\theta$ = - $3.4159$ , $\theta$ belongs to Q II
We will find reference angle of $\theta$ first, using calculator in degree mode by the$\frac{1}{x}$ and $\cos^{-1}$ key with the positive value $3.4159$ as $\cos\theta$ = $\frac{1}{\sec\theta}$-
$3.4159$ → $\frac{1}{x}$ → $\cos^{-1}$→→ 72.977416435
i.e. reference angle of $\theta$ = $72.977416435^{\circ}$
The desired angle $\theta$ is in Q II, whose reference angle is $73^{\circ}$.
Also $0^{\circ}\leq \theta\lt 360^{\circ}$
Therefore-
$\theta$ = $180^{\circ} - 72.977416435^{\circ}$
= $107.02258357^{\circ}$
= $107^{\circ}$
(to the nearest tenth of a degree)