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The size of the angle is 60°.

Step-by-step explanation:

Let name the regular hexagon as ABCDEF and the Rhombus as ABOF.

Let angle AFO and angle ABO be y (opposite angles of a rhombus are equal)

To Find :

Solution:

As we know polygon ABCDEF is a regular hexagon then we have

As it is a regular hexagon all angles are equal

∴

i.e

Now quadrilateral ABOF is a rhombus given.

Therefore. Opposite angles of rhombus are equal.

∴

Now in a quadrilateral sum of all the angles is 360°

∴

But

Therefore the size of angle x is 60°