Answer:
33. 15 sides
34. 24 sides
35. 40 sides
36. 60 sides
Step-by-step explanation:
You want the number of sides of a regular polygon with interior angles of 156° or 165°, and with exterior angles of 9° or 6°.
Sides and angles
The sum of all exterior angles is 360°, so the relationship between the number of sides n and the measure of exterior angle θ is ...
n = 360°/θ
Each exterior angle is the supplement of the adjacent interior angle. For interior angle φ, the corresponding number of sides is ...
n = 360°/(180° -φ)
33. φ = 156°
n = 360°/(180° -156°) = 360/24 = 15
The polygon has 15 sides.
34. φ = 165°
n = 360°/(180° -165°) = 360/15 = 24
The polygon has 24 sides.
35. θ = 9°
n = 360°/9° = 40
The polygon has 40 sides.
36. θ = 6°
n = 360°/6° = 60
The polygon has 60 sides.
