Question

the ratio of inner angle of an equilateral polygon and angle of the outer polygon is 1:2 .what is the number of arms​

Answer 1

let the interior angle of the regular polygon be X.
therefore, the exterior angle is X/4.
Exterior angle + adjacent interior angle =180
0

4
X
​
+X=180
0

4
5X
​
=180
0

X=180
0
×
5
4
​

=144
0

the interior angle is 144
0

the exterior angle is 36
0

n=
exteriorangle
360
0

​

=
36
0

360
0

​
=10
The number of sides of a regular polygon is

Answer 2

Answer:

Interior angle = 120

Exterior angle = 60

The number of arms of the polygon is 6

Step-by-step explanation:

Exteroir angle + Adjacent angle = 180°

$\frac{x}{2} + x = 180$

$\frac{3}{2} = 180 \\x = 180 * \frac{2}{3} \\ = 120$

Interior angle = 120

Exterior angle = $\frac{120}{2}$ = 60

$\frac{360}{Exterior angle } = \frac{360}{60} \\n = 6$

The number of arms of the polygon is 6