Based on the diagram showing a rhombus inside a regular pentagon, the size of angle x is 18°.
In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:
Sum of interior angles = 180 × (n - 2)
Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.
Sum of interior angles = 180 × (5 - 2)
Sum of interior angles = 180 × 3
Sum of interior angles = 540°.
Therefore, the measure of each interior angle is given by;
Interior angle of a pentagon = 540°/5
Interior angle of a pentagon = 108°
A rhombus is a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent, with a measure of 90 degrees;
x + 90 = 108
x = 108 - 90
x = 18°