Answer
$13^o$
Work Step by Step
RECALL:
An angle $\theta$, where $360^o \lt \theta \lt 720^o$, is coterminal with:
$\theta - 360^o$
Thus, the given angle is coterminal with:
$=553^o - 360^o
\\=193^o$
$553^o$ is coterminal with $193^o$.
$193^o$ is in Quadrant III so $553^o$ is also in Quadrant III.
RECALL:
The following are the means on how to find the reference angle of an angle $0\leq \theta \lt 360^\circ$ based on its position:
(1) Quadrant I: $\theta$ (itself)
(2) Quadrant II: $180^o-\theta$
(3) Quadrant III: $\theta - 180^o$
(4) Quadrant IV: $360^o-\theta$
Use formula (3) above to obtain:
reference angle of $553^o$ = reference angle of $193^o$, which is $193^o - 180^o = 13^o$
