If each angle of a regular polygon measures 150°, how many sides does it have?
If each internal angle of a regular polygon measures 150°, each external angle measures (180-150)=30°.
Since the sum of all polygons add up to 360° and for a regular polygon of n-sides, each exterior angle (E=30°) is equal, we arrive at the relation:
nE=360
n(30)=360
Solve for n.
The name of the polygon starts with the letter 'd'.
Dodecagon
To determine the number of sides in a regular polygon, we can use the formula:
n = 360° / interior angle
In this case, the interior angle of the regular polygon is given as 150°. Substituting this value into the formula, we have:
n = 360° / 150°
To calculate this division, simply divide 360 by 150:
n = 2.4
Since it does not make sense for a polygon to have a fractional number of sides, we round the result to the nearest whole number. In this case, the nearest whole number is 2.
Therefore, a regular polygon with each angle measuring 150° has 2 sides.