The measure of each interior angle of a regular polygon can be expressed as x-5 and the number of sides by 10x. Determine the following the number of degrees in each exterior angle

  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

squares, rhombus, rectangles