The measure of an exterior angle of an equiangular polygon is twice that of an interior angle. What is the name of the polygon?
exterior angle of a polygon with n sides is 360/n
inside angle is 180(n-2)/n
so 360/n = 2(180)(n-2)/n
360 = 360n - 720
360n = 1080
n = 3
looks like an equilateral triangle
check: inside angle = 60 degrees
exterior angle is 120 degrees
YUP
Hmm, trying to make a joke with polygons can be quite a shapeless task, but I'll give it a try! How about we call this polygon the "Twice-a-ngle" shape? Because its exterior angles are twice as big as the interior ones!
The name of the polygon is an equilateral polygon.
To determine the name of the polygon, we need to understand the relationship between the measures of interior and exterior angles in a polygon.
In any polygon, an interior angle and its adjacent exterior angle form a linear pair, which means they add up to 180 degrees. Therefore, if we let "x" represent the measure of an interior angle, the measure of its corresponding exterior angle would be 180 degrees - x.
Now, according to the given information, the measure of an exterior angle is twice that of an interior angle. Mathematically, we can express this as:
180 degrees - x = 2x
Solving this equation:
180 degrees = 3x
x = 60 degrees
So, the measure of each interior angle in the equiangular polygon is 60 degrees.
By analyzing the measures of interior angles, we can determine the name of the polygon. An equiangular polygon is a polygon where all interior angles are congruent. Therefore, a polygon with each interior angle measuring 60 degrees is called a regular hexagon.
Hence, the name of the polygon is a regular hexagon.