12. The ratio of an interior angle to an exterior angle of an n-sided regular polygon is 13:2. Find the value of n.
of its exterior angles, find the
Answers
Step-by-step explanation:
Given:-
The ratio of an interior angle to an exterior angle of an n-sided regular polygon is 13:2.
To find:-
Find the value of n. and Find its exterior and interior angles
Solution:-
The ratio of an interior angle to an exterior angle of an n-sided regular polygon is 13:2.
We know that the interior angle of an n-sided polygon = [(n-2)/n]×180°
We know that the exterior angle of an n-sided polygon = 360°/n
Thier ratio = [(n-2)/n]×180° : (360°/n)
=>(n-2)×180°/n : 360°/n
=>(n-2)/n : 2/n
=>(n-2) : 2
According to the given problem
The ratio is 13:2
=>(n-2) : 2 = 13:2
=>(n-2)/2 = 13/2
On applying cross multiplication then
=>(n-2)×2 = 13×2
=>2n-4 = 26
=>2n = 24+6
=>2n = 30
=>n=30/2
=>n = 15
The exterior angle = 360°/15 = 24°
The interior angle = (15-2)×180°/15
=>13×180°/15
=>13×12°
=>156°
Answer:-
The value of n = 15
The exterior angle of the polygon = 24°
The interior angle of the polygon = 156°
Used formulae:-
- an exterior angle of an n-sided regular polygon is 360°/n
- an interior angle of an n-sided regular polygon is [(n-2)/n]×180°