Answer:
0.1948° in each exterior angle
Step-by-step explanation:
The exterior angle measure is 360° divided by the number of sides. Here, that is 10x, so the exterior angle is ...
360°/(10x) = 36°/x
The measure of the interior angle is the supplement of the exterior angle, so we have ...
x -5 = 180 -(36/x)
x(x -5) = 180x -36 . . multiply by x
x^2 -185x = -36 . . . . . subtract 180x
x^2 -185x +8556.25 = -36 +8556.25 . . . . complete the square
(x -92.5)^2 = 8520.25
x -92.5 ≈ ±92.3052
x ≈ 184.8052 or 0.19480
It does not make any sense for the number of sides to be 10·0.1948 = 1.948, so we assume the number of sides is 184.8052·10 = 1848.
Then the number of degrees in each exterior angle is ...
36°/184.8052 = 0.1948
