Answer: x = 60°
Step-by-step explanation:
The rest of the question is the attached figure.
Given: A rhombus inside a regular hexagon, work out the angle x.
As shown
ABCDEF is a regular hexagon.
The regular hexagon have 6 congruent angles, and the sum of the interior angles is 720°
So, the measure of one angle of the regular hexagon = 720/6 = 120°
So, ∠F = ∠BAF = 120°
AFEG is a rhombus.
The rhombus have 2 obtuse angles and 2 acute angles.
∠F is one of the obtuse angles of the rhombus = 120°
∠F and ∠FA G are supplementary angles
So, ∠F + ∠FA G = 180°
∴ ∠FA G = 180° - ∠F = 180 - 120 = 60°
∴ x = ∠GAB = ∠BAF - ∠FA G = 120 - 60 = 60°
So, the measure of the angle x = 60°
