Final answer:
To calculate the measure of one interior angle in a regular dodecagon, we use the sum of interior angles, which is (12-2)×180°, and divide by the number of sides (12), resulting in 150° per angle.
Step-by-step explanation:
The measure of one interior angle in a regular dodecagon (a 12-sided polygon) can be calculated using the formula for the sum of interior angles (n-2)×180°, where n is the number of sides in the polygon.
For a dodecagon, n = 12. Thus, the sum of the interior angles is (12-2)×180° = 1,800°. To find the measure of one interior angle in a regular dodecagon, we divide the sum of the interior angles by the number of angles, which is equal to the number of sides. Therefore, one interior angle measures 1,800°/12 = 150°.