Answer
$74.7^{\circ}$
Work Step by Step
Given-
$\cos\theta$ = $0.2644$ , $\theta$ belongs to Q I and $0^{\circ}\leq \theta\lt 360^{\circ}$
We will find reference angle of $\theta$ first, using calculator in degree mode by the $\cos^{-1}$ key with the value $0.2644$-
$0.2644$ → $\cos^{-1}$→→ 74.668696243
i.e. reference angle of $\theta$ = $74.7^{\circ}$ (to the nearest tenth of a degree)
The desired angle $\theta$ is in Q I, whose reference angle is $74.7^{\circ}$.
Therefore-
$\theta$ = $74.7^{\circ}$ ( for QI ref. angle of $\theta$ = $\theta$ as $0^{\circ}\leq \theta\lt 360^{\circ}$ )