Let,
x = interior angle
y = exterior angle
Conditions:
The exterior angle measures twice its interior.
y = 2x
Properties:
interior and exterior angles of polygons are supplementary.
x + y = 180°
but,
y = 2x
now solve for interior angle x,
x + y = 180
x + 2x = 180
3x = 180
x = 60°
solve for exterior angle y,
y = 2x
y = 2(60)
y = 120°
find number of sides (n) using each exterior angle y,
Each exterior angle = 360/n
120 = 360/n
n = 360/120
n = 3
So number of sides of regular polygon is 3.
So it is a triangle ∆.
Alternate solution using each interior angle x,
Each interior angle = [(n - 2)×180] / n
60 = [(n - 2)×180] / n
60n = 180n - 360
180n - 60n = 360
120n = 360
n = 360/120
n = 3
same answer, n = 3
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