Answer
$277^{\circ}$
Work Step by Step
Given-
$\cot\theta$ = - $0.1234$ , $\theta$ belongs to Q IV
We will find reference angle of $\theta$ first, using calculator in degree mode by the$\frac{1}{x}$ and $\tan^{-1}$ key with the positive value $0.1234$ as $\tan\theta$ = $\frac{1}{\cot\theta}$
$0.1234$ → $\frac{1}{x}$ → $\tan^{-1}$→→ 82.965264244
i.e. reference angle of $\theta$ = $82.965264244^{\circ}$
The desired angle $\theta$ is in Q IV, whose reference angle is $82.965264244^{\circ}$.
Also $0^{\circ}\leq \theta\lt 360^{\circ}$
Therefore-
$\theta$ = $360^{\circ} - 82.965264244^{\circ}$
= $277.03473576^{\circ}$
= $277^{\circ}$
(to the nearest tenth of a degree)
