Geometry and TrigonometryEasy–MediumSides of a regular polygon from its exterior angle
Geometry and Trigonometry practice question
The exterior angles of any polygon, one at each vertex, add to 360°. Each exterior angle of a certain regular polygon measures 45°. How many sides does the polygon have?
Answer: 8
All exterior angles of a regular polygon are equal, so their number is 360 / 45 = 8. The polygon is an octagon.
Common wrong answers
- If you answered 4
- 4 is 180 / 45. Exterior angles add to 360, not 180.
- If you answered 6
- 6 sides would give exterior angles of 360 / 6 = 60°, not 45°.
- If you answered 45
- 45 is the size of one exterior angle in degrees, not the count of sides.
More Geometry and Trigonometry questions
- Easy–Medium
A circle has a radius of 6. What is its area? (Use A = πr².) - Easy–Medium
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse? - Easy–Medium
A circle has a radius of 5. What is its circumference? (Use C = 2πr.) - Easy–Medium
What is the midpoint of the segment joining the points (2, 3) and (8, 11)? - Easy–Medium
What is the measure, in degrees, of angle B? - Easy–Medium
What is the area, in square centimeters, of the trapezoid?
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