Advertisements
Advertisements
Question
The ratio between the exterior angle and the interior angle of a regular polygon is 1 : 4. Find the number of sides in the polygon.
Advertisements
Solution
Let exterior angle = x° & interior angle = 4x°
∴ 4x + x = 180°
5x = 180°
x = 36°
∴ Each exterior angle = 36°
Let no.of sides = n
∴ `360^circ/"n" = 36^circ`
n = `360^circ/36^circ`
n = 10
APPEARS IN
RELATED QUESTIONS
Fill in the blanks :
In case of regular polygon, with :
| No.of.sides | Each exterior angle | Each interior angle |
| (i) ___8___ | _______ | ______ |
| (ii) ___12____ | _______ | ______ |
| (iii) _________ | _____72°_____ | ______ |
| (iv) _________ | _____45°_____ | ______ |
| (v) _________ | __________ | _____150°_____ |
| (vi) ________ | __________ | ______140°____ |
Find the number of sides in a regular polygon, if its interior angle is: 135°
Is it possible to have a regular polygon whose interior angle is : 170°
AB, BC and CD are three consecutive sides of a regular polygon. If angle BAC = 20° ; find :
(i) its each interior angle,
(ii) its each exterior angle
(iii) the number of sides in the polygon.
The difference between the exterior angles of two regular polygons, having the sides equal to (n – 1) and (n + 1) is 9°. 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.
Calculate the number of sides of a regular polygon, if: its interior angle is five times its exterior angle.
Calculate the number of sides of a regular polygon, if: the ratio between its exterior angle and interior angle is 2: 7.
Is it possible to have a regular polygon whose exterior angle is: 36°
What is the sum of all exterior angles of any regular polygon?
