Answer:
x=30
Step-by-step explanation:
Since this a regular hexagon, each angle measure is congruent.
A hexagon interior angles add to be
([tex]{6 - 2}) \times 180 = 720[/tex]
However, in the triangle, only part of angle b and angle f is in the triangle. However angle a is fully in the triangle so
Angle A=120.
So using the triangle interior theorem, angle b and f must add up to 180.
[tex]120 + x + y = 180[/tex]
However, since this is a regular hexagon, the sides are equal so this is a isoceles triangle.
Using the base isoceles triangle theorem, angle b and angle f of the triangle must be equal so
[tex]x = y[/tex]
[tex]120 + 2x = 180[/tex]
[tex]2x = 60[/tex]
[tex]x = 30[/tex]
