Since each vertex of a pentagon has an angle measure of 108°, the size of angle x is 54°.
How to determine the size of angle x?
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°.
Measure of each interior angle = 540°/5
Measure of each interior angle = 108°
Since each vertex of a pentagon has an angle measure of 108°, we would divide the interior angle by 2;
x = 108/2
x = 54
Complete Question;
The diagram shows a regular pentagon with centre 0. Work out the size of angle x.