Advertisements
Advertisements
Question
The sum of interior angles of a regular polygon is thrice the sum of its exterior angles. Find the number of sides in the polygon.
Advertisements
Solution
Sum of interior angles = 3 x Sum of exterior angles
Let exterior angle = x
The interior angle = 3x
x + 3x=180°
⇒ 4x = 180°
⇒ x = `180/4`
⇒ x = 45°
Number of sides = `360/45 = 8`
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°
Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.
Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate 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.
Calculate the number of sides of a regular polygon, if: its exterior angle exceeds its interior angle by 60°.
Is it possible to have a regular polygon whose interior angle is: 155°
Is it possible to have a regular polygon whose exterior angle is: 100°
If each interior angle of a regular polygon is 144°, what is its corresponding exterior angle?
Which formula correctly represents the sum of interior angles of an n-sided polygon?
