Answer:
x = 52°
Step-by-step explanation:
The sum of the exterior angles of a polygon
The sum of the exterior angles of a polygon is always 360° regardless of the number of sides.
The figure shows five angles that are exterior to the central pentagon.
The sum of all those angles is:
52 + 2x + 88 + x + 10 + x + 2
And that sum must be equal to 360, thus:
52 + 2x + 88 + x + 10 + x + 2 = 360
Simplifying:
4x + 152 = 360
Subtracting 152:
4x = 208
Dividing by 4:
x = 208/4 = 52
x = 52°
