Final answer:
To determine the value of x in the equation representing a regular decagon's exterior angle measure (3x+6°), we use the fact that the sum of a polygon's exterior angles is 360°. Dividing 360° by the number of sides of the decagon (10) gives us the measure of one exterior angle (36°). Solving 3x+6° = 36° yields x = 10.
Step-by-step explanation:
The question asks for the value of x in the equation representing the measure of an exterior angle of a regular decagon, which is given as 3x+6°. We know that the sum of the exterior angles of any polygon is 360°. For a regular decagon, which has 10 sides, each exterior angle has the same measure. To find the measure of one exterior angle, we divide 360° by the number of sides (10), obtaining 36° as the measure of one exterior angle. Thus, to solve the equation 3x+6° = 36° for x, we subtract 6° from both sides to get 3x = 30°, and then divide both sides by 3 to isolate x, resulting in x = 10°. Therefore, the value of x is 10.