Question

The diagram shows a rhombus inside a regular hexagon work out the angle x

Answer 1

Answer:

x = 60°

Step-by-step explanation:

The rest of the question is the attached figure.

And it is required to find the angle x.

As shown, a rhombus inside 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°

The rhombus have 2 obtuse angles and 2 acute angles.

one of the obtuse angles of the rhombus is the same angle of the regular hexagon.

So, the measure of each acute angle of the rhombus = 180 - 120 = 60°

So, the measure of each acute angle of the rhombus + the measure of angle x = the measure of one angle of the regular hexagon.

So,

60 + x = 120

x = 120 - 60 = 60°

So, the measure of the angle x = 60°