-401.07 degrees is the same as -41.07 degrees. That would be in the fourth quadrant. There should have been a figure associated with this problem showing the direction and place that the arc was located.
Let's just consider the size of the subtended angle.
An 8 cm arc on a 15 cm radius is 8/15 radian or
(8/15)(180/pi) = 96/pi = 30.56 degrees
I have no idea how you or your textbook came up with -401.07 degrees
Find the degree measure of the central angle whose intercepted arc measures 8cm in a circle of radius 15cm.
Answer: -401.07 degrees
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