Calculating Regular Polygon Sides
The problem asks for the number of sides of a regular polygon given that each exterior angle measures $40^\circ$.
Exterior Angle Formula
For any convex polygon, the sum of the exterior angles is $360^\circ$. In a regular polygon with 'n' sides, all exterior angles are equal. The formula relating the number of sides (n) and the measure of each exterior angle is:
$ \text{Exterior Angle} = \frac{360^\circ}{n} $
Solving for Number of Sides (n)
We are given that the exterior angle is $40^\circ$. We can substitute this value into the formula and solve for 'n':
- Set up the equation: $ 40^\circ = \frac{360^\circ}{n} $
- Rearrange the equation to solve for 'n': $ n = \frac{360^\circ}{40^\circ} $
- Calculate the value of 'n': $ n = 9 $
Therefore, the regular polygon has 9 sides.
Similar Questions
- If the sum of the interior angles of a regular polygon is equal to four times the sum of its exterior angles, then what is the number of diagonals in the polygon?
- Find the ratio of the measure of an angle of a regular pentagon to that of a regular octagon.
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- In a polygon, the sum of the interior angles is triple the sum of the exterior angles. The number of sides is:
- What is the measure of each exterior angle of a regular octagon?
- The difference between the interior and exterior angles at a vertex of a regular polygon is $140^\circ$. The number of sides of the polygon is:
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- If the side of an equilateral triangle is 2 cm, then find the area and the altitude of the triangle.
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Important Questions from Geometry
If the angles of a triangle are in the ratio of 2:3:4, then the difference of the measure of greatest angle and smallest angle is
In ΔABC, ∠A = 90°, AD ┴ BC and AD = BD = 2 cm. The length of CD is
How many lines of symmetry does a rectangle have?
The number of diagonals in each face a cube is
Which of the following is/are the geometric figures with the line of symmetry?
I. Rectangle
II. Isosceles triangle
