Answer:
150 cm
Step-by-step explanation:
The total of exterior angles is 360°. We can use this fact to find the number of sides. The perimeter is the total length of all of the congruent sides.
Exterior angles
The measure of an exterior angle of the regular polygon is the supplement of the adjacent interior angle:
exterior angle = 180° -156° = 24°
The total of n of these angles is 360°, so n is ...
24°×n = 360°
n = 360°/24° = 15
The polygon has 15 exterior angles, hence 15 sides
Perimeter
The perimeter is the total length of the 15 congruent sides:
P = 15×(10 cm) = 150 cm
The perimeter of the regular polygon is 150 cm.
