Answer
$50^{\circ}$
Work Step by Step
The reference angle of an angle $0 \leq \theta \lt 2\pi $ based on its position can be computed by using the following steps:
a) Quadrant- I: $\theta $
b) Quadrant -II: $(\pi-\theta)$
c) Quadrant- III: $(\theta - \pi)$
d) Quadrant - IV: $(2\pi - \theta)$
First, make the angle positive, by adding $360^{\circ}$ twice:
$-410^{\circ}+2*360^{\circ}=310^{\circ}$
We are in quadrant 4, so subtract from 360:
$360^{\circ}-310^{\circ}=50^{\circ}$
