Final answer:
The sum of 10 interior angles of a regular dodecagon is 1500°, calculated by finding the sum of all interior angles (1800°) and then determining the measure of one angle (150°) since it is a regular polygon with equal angles, and multiplying this by 10.
Step-by-step explanation:
To calculate the sum of 10 interior angles of a regular dodecagon, you first need to understand how to find the sum of all the interior angles of a dodecagon. The formula for the sum of interior angles of any polygon is given by S = (n-2) × 180°, where S represents the sum of interior angles and n is the number of sides in the polygon. Since a dodecagon has 12 sides, plugging into the formula gives us:
S = (12-2) × 180°
S = 10 × 180°
S = 1800°
The sum of all interior angles of a regular dodecagon is 1800°. However, the student asks for the sum of 10 of the interior angles of a regular dodecagon, not all 12. Since the dodecagon is regular, all interior angles are equal, so we divide the total sum by the number of angles to find the measure of one angle:
Measure of one interior angle = S / n
Measure of one interior angle = 1800° / 12
Measure of one interior angle = 150°
To find the sum of 10 of these angles, we then simply multiply the measure of one interior angle by 10:
Sum of 10 interior angles = 150° × 10
Sum of 10 interior angles = 1500°