Answer
$156.4^{\circ}$
Work Step by Step
Given-
$\csc\theta$ = $2.4957$ , $\theta$ belongs to Q II and $0^{\circ}\leq \theta\lt 360^{\circ}$
We will find reference angle of $\theta$ first, using calculator in degree mode by the$\frac{1}{x}$ and $\sin^{-1}$ key with the value $2.4957$ as $\sin\theta$ = $\frac{1}{\csc\theta}$
$2.4957$ → $\frac{1}{x}$ → $\sin^{-1}$→→ 23.621269856
i.e. reference angle of $\theta$ = $23.6^{\circ}$ (to the nearest tenth of a degree)
The desired angle $\theta$ is in Q II, whose reference angle is $23.6^{\circ}$.
Also $0^{\circ}\leq \theta\lt 360^{\circ}$
Therefore-
$\theta$ = $180^{\circ} - 23.6^{\circ}$
= $156.4^{\circ}$
