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
- The adjacent sides of a parallelogram are $4a$ and $3a$. If the angle between them is $60^{\circ}$, then one of the diagonals of the parallelogram will be:
- Every interior angle of a regular octagon is $135^\circ$. Find the exterior angle of the octagon.
- 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 $\angle RQP$.
- ABC is an equilateral triangle and O is its circumcentre. If the side of triangle is 6 cm, then the $\angle BOC$ is:
- 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:
- 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.
- 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:
Important Questions from Geometry
ABCDEF is a regular hexagon. Side of the hexagon is 36 cm. What is the area of the triangle AOB ?
If ∆ABC ~ ∆DEF, and BC = 4 cm, EF = 5 cm and the area of triangle ABC = 80 cm 2, then the area of the triangle DEF is:
If Δ ABC is right angled at B, AB = 12 cm and ∠CAB = 60°, determine the length of BC.
If ΔABC and ΔDEF are congruent triangles, then which of the following is FALSE?
D and E are points on the sides AB and AC, respectively, of ΔABC such that DE is parallel to BC and AD ∶ DB = 7 ∶ 9. If CD and BE intersect each other at F. then find the ratio of areas of ΔDEF and ΔCBF.
