Answer
$220^{\circ}$
Work Step by Step
Given-
$\cos\theta$ = - $0.7660$ , $\theta$ belongs to Q III
We will find reference angle of $\theta$ first, using calculator in degree mode by the $\cos^{-1}$ key with the positive value $0.7660$-
$0.7660$ → $\cos^{-1}$→→ 40.003961337
i.e. reference angle of $\theta$ = $40^{\circ}$ (to the nearest degree)
The desired angle $\theta$ is in Q III, whose reference angle is $40^{\circ}$. Therefore-
$\theta$ = $ 180^{\circ} + 40^{\circ}$
= $220^{\circ}$
