the number of sides of an n-gon if the sum of the interior angle is 1800°
Answers
Answer:
The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.
Answer:
The sum of exterior angle and its adjacent interior is 180
0
, that is,
e+i=180
0
Since each exterior angle is equal to twice its adjacent interior angle, therefore, substitute 2i=e or i=
2
e
.
e+
2
e
=180
0
⇒
2
2e+e
=180
0
⇒
2
3e
=180
0
⇒3e=180
0
×2
⇒3e=360
0
⇒e=
3
360
0
=120
0
We know that the measure of exterior angle is e=(
n
360
)
0
where n is the number of sides.
Here, it is given that the exterior angle is e=120
0
, therefore,
n=
e
360
=
120
360
=3
Hence, the number of sides is 3