Polygon Sides Calculation Using Interior Angle
To determine the number of sides of a regular polygon when given the measure of each interior angle, it's efficient to use the exterior angle property.
Exterior Angle Calculation
The sum of an interior angle and its adjacent exterior angle for any polygon is $180^\circ$. Given the interior angle is $144^\circ$, we find the exterior angle:
Exterior Angle = $180^\circ - 144^\circ = 36^\circ$
Number of Sides Calculation
The sum of all exterior angles of any convex polygon is $360^\circ$. For a regular polygon with '$n$' sides, each exterior angle measures $\frac{360^\circ}{n}$.
Setting the calculated exterior angle equal to the formula:
$36^\circ = \frac{360^\circ}{n}$
Solving for '$n$':
$n = \frac{360^\circ}{36^\circ}$
$n = 10$
Result
The regular polygon has 10 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:
- 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:
- The area of an isosceles right angle triangle is $81 \text{ cm}^2$ . Find the length of its hypotenuse.
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.
