Question

If a rhombus is inside a regular hexagon, what is the size of x

Answer 1

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°