Advertisements
Advertisements
Question
Is it possible to have a regular polygon whose interior angle is: 155°
Advertisements
Solution
No. of. sides = n
Each interior angle = 155°
∴ `(("2n" - 4) xx 90^circ)/"n" = 155^circ`
180n - 360° = 155n
180n - 155n = 360°
25n = 360°
n = `(360°)/(25°)`
n = `72^circ/5`
Which is not a whole number.
Hence, it is not possible to have a regular polygon whose interior angle is 155°.
APPEARS IN
RELATED QUESTIONS
Is it possible to have a regular polygon whose each exterior angle is: 80°
Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.
The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.
Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.
If the difference between the exterior angle of a 'n' sided regular polygon and an (n + 1) sided regular polygon is 12°, find the value of n.
Three of the exterior angles of a hexagon are 40°, 51 ° and 86°. If each of the remaining exterior angles is x°, find the value of x.
The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.
Find a number of side in a regular polygon, if it exterior angle is: 30°.
If each interior angle of a regular polygon is 144°, what is its corresponding exterior angle?
What is the sum of all exterior angles of any regular polygon?
