Answer:
12.gon - An interior angle measures 150°
Called a Dodecagon, the sum of all of its interior angles is 1,800° therefore each individual angle is;
= 1,800/12
= 150°
15-gon - An exterior angle measures 24°
The sum of all the exterior angles of a polygon add up to 360 so a polygon with a 24° exterior angle is;
= 360/24
= 15°
16-gon - The sum of the interior angles is 2,520°
Known as a hexadecagon, each interior angle of this polygon is a 157.5° and when added up this comes to 2,520°.
18-gon - An interior angle measures 160°
The formula for calculating the interior angle of a polygon is;
Angle = (n−2) × 180° / n
160 = (n−2) × 180° / n
160n = 180n - 360
360 = 20n
n = 18
Other tiles
The sum of the exterior angles is 180º - all exterior angles must add up to 360º so this does not exist.
The sum of the interior angles is 2,160° - this is a 14 sided polygon which is not listed in the options.
