Determine sides of polygon

Question

Two of the interior angle of a polygon are 50 degrees and 150 degrees. Given that, all the remaining sides are equal in length forming an exterior angle of 20 degrees. Calculate the number of sides and state the name of the polygon.

Answer 1

the sum of the exterior angles of any polygon is 360°

if one interior angle is 50°, then the exterior angle must be 130° because the interior angle and its exterior angle sum to 180°

therefore, if another interior angle is 150°, then the exterior angle is 30°

so we have 130°+30°=160°

360°-160°=200° remaining for the other exterior angles

each exterior angle equals 20° so 200°/20°=10 angles and therefore 10 sides

taking the original 2 sides with their interior angles plus these 10 sides gives us 12 sides

a 12 sided polygon is called a dodecagon