maths
The interior angle of a regular polygon is 150°
How many sides does the polygon have?
180°(n - 2)/n = 150°
(n - 2)/n = 150°/180° = 5/6
5n = 6(n - 2)
n = 12
The polygon has 12 sides.
Sum of interior angles = 180(n – 2).
Therefore, each internal angle will be [180(n - 2)]/n
150 = [180(n - 2)]/n
150 = (180n - 360)/n
150n = 180n - 360
30n = 360
check
(n - 2)180
= (12 - 2)180
= 10 x 180
=1800
1800/12 = 150
ANS 12
If the interior angle is 150°, the exterior angle is 30° (supplementary).
And all the exterior angles in a polygon add up to 360°, so there must be 12 sides.
360° / 30° = 12 sides
Answer:
Regular dodecagon with 12 sides
15 sides
ask vsauce.
It has 12 sides because there are 180 degrees on a straight line and 180-150 = 30 and there are 360 degrees around any polygon and so 360/30 = 12 sides
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Answers & Comments
The interior angle of a regular polygon is 150°
How many sides does the polygon have?
180°(n - 2)/n = 150°
(n - 2)/n = 150°/180° = 5/6
5n = 6(n - 2)
n = 12
The polygon has 12 sides.
Sum of interior angles = 180(n – 2).
Therefore, each internal angle will be [180(n - 2)]/n
150 = [180(n - 2)]/n
150 = (180n - 360)/n
150n = 180n - 360
30n = 360
n = 12
check
(n - 2)180
= (12 - 2)180
= 10 x 180
=1800
1800/12 = 150
ANS 12
If the interior angle is 150°, the exterior angle is 30° (supplementary).
And all the exterior angles in a polygon add up to 360°, so there must be 12 sides.
360° / 30° = 12 sides
Answer:
Regular dodecagon with 12 sides
15 sides
ask vsauce.
It has 12 sides because there are 180 degrees on a straight line and 180-150 = 30 and there are 360 degrees around any polygon and so 360/30 = 12 sides