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
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- PQ is a diameter of circle whose centre is O. If a point R lies on a circle and $\angle RPO$ is $42^\circ$, then find $\angle RQP$.
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- If every interior angle of a regular polygon is $144^\circ$, then the polygon has ______ sides.
- The ratio of the numbers of sides of two regular polygons is $1 : 2$. If each interior angle of the first polygon is $140^\circ$, then the measure of each interior angle of the second polygon is:
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Important Questions from Geometry
The sides of a triangle are in the ratio 6 : 4 : 3 and its perimeter is 104 cm. The length of the longest side (in cm) is:
An isosceles right-angled triangle has hypotenuse length as 10 units. What is the area of the triangle (in square units)?
Two circles of radii 16 cm and 4 cm, respectively, touch each other externally at Point A. PQ is the direct common tangent of these circles with centres C1 and C2, respectively. What is the length of PQ?
Let C be a circle with center O and AB be a chord of C such that the length of AB is equal to the radius of C. Let D be any point on the major arc of AB. Find ∠AOB and ∠ADB, respectively.
The centres of two circles are 84 cm apart. If the radii of these two circles are 38 cm and 26 cm, respectively, then which of the following options gives the length (in cm) of a direct common tangent of these two circles?
