Question

in the regular nonagon shown, what is the measure of angle x?
36°
40°
45°
60°

Explanation:

Step1: Recall the formula for the central angle of a regular polygon

The measure of the central angle (the angle subtended at the center by one side) of a regular \( n \)-sided polygon is given by \( \frac{360^\circ}{n} \). For a regular nonagon, \( n = 9 \).

Step2: Calculate the central angle

Substitute \( n = 9 \) into the formula: \( \frac{360^\circ}{9}=40^\circ \). The angle \( x \) in the diagram (which is the exterior angle or related to the central angle for a regular polygon's side - related angle) is equal to this central angle in the context of a regular nonagon's side - to - side angle calculation.

Answer:

\( 40^\circ \) (corresponding to the option "40°")