Answer
reference angle = $8.3^o$
Refer to the image below for the drawing.
Work Step by Step
Convert the angle measurement to degrees by multiplying $40'$ by $\dfrac{1^o}{60'}$ to obtain:
$171^o + 40' \cdot \dfrac{1^o}{60'}=171^o + 0.\overline{6}\approx 171.7^o$
The angle is positive so from the positive x-axis, move $171.7$ degrees counterclockwise.
(refer to the attached image in the answer part above)
The terminal side of the angle is in Quadrant II.
The reference angle of an angle $\theta$ in Quadrant II can be found using the formula $180^o-\theta$
Thus, the reference angle of the given angle is:
$=180^o -171.7^o
\\=8.3^o$
