IF it is a regular polygon
central angle of the 14 triangles created from the center is 360/n = 180/7
All triangles are isosceles.... so one non central angle is (180 -180/7)/2
But that is only 1/2 of one of the interior angles so multiply by 2
= 180 - 180/7 <--- Answer
Another way is the total of all angles of the 14 triangles formed from the center is 14(180) But the center is a circle = 360 so the sum of the interior angles is
14(180) - 360. A little alg shows this is (14 - 2)180 A FORMULA FROM GEOMETRY. (n-2)180
So if all = 12(180) then one will be 12(180)/14 <--- Answer
Only if the polygon is "regular".
Only when it is a regular polygon that all interior angles are of equal measure
Only when the polygon is a regular convex polygon. Such as an equilateral triangle, or a square, or a regular pentagon.
A regular polygon with each interior angle measuring 120 degrees is a hexagon.
Each interior angle will measure 162 degrees
A regular polygon having an interior angle measure of 168o has 30 sides and is called a triacontagon.
Only if the polygon is "regular".
Only when it is a regular polygon that all interior angles are of equal measure
If the measure of an interior angle of a regular polygon is 140o, the polygon is a nonagon (sometimes called an ennagon) having 9 sides.
The measure of each interior angle of a fifteen sided regular polygon, a pendedecagon, is 156o.
A 13 sided regular polygon
The interior angle of an octdecagon, an 18 sided regular polygon, is 160o.
A regular polygon with 4 sides is a square. The measure of any interior angle of a square is 90 degrees.
A regular hexagon.
Only if the polygon is a "regular" one.
Only when the polygon is a regular convex polygon. Such as an equilateral triangle, or a square, or a regular pentagon.
A regular polygon with each interior angle measuring 120 degrees is a hexagon.