To find the measure of angle X in a regular nonagon, we need to use the formula for calculating the interior angle of a regular polygon. The formula for the measure of each interior angle in a regular polygon is:
Interior Angle = (n – 2) × 180° / n
where n is the number of sides of the polygon. For a nonagon, n = 9.
Plugging in the value:
Interior Angle = (9 – 2) × 180° / 9
Interior Angle = 7 × 180° / 9
Interior Angle = 1260° / 9
Interior Angle = 140°
Therefore, the measure of angle X in the regular nonagon is 140°.