IF ONE OF THE INTERIOR ANGLES OF A REGULAR POLYGON IS TO BE EQUAL TO (9/8) TIMES OF ONE OF THE INTERIOR ANGLES OF A REGULAR HEXAGON,THEN THE INTERIOR SIDES OF THE POLYGONS IS .......?
Let the interior angle of regular polygon be x. According to the question,
x∘
=
8
9
×120
∘
=135
∘
135
∘
=
n
(n−2)×180
∘
45n=360
∘
Hence, the number of sides is 8.
To find the length of the interior sides of the polygons, we need to know the relationship between the interior angles and the sides of regular polygons.
In a regular polygon, all interior angles are equal, and the sum of the interior angles is given by the formula:
Sum of interior angles = (n - 2) * 180 degrees
Where n is the number of sides of the polygon.
For a regular hexagon (n = 6), each interior angle is:
Interior angle of hexagon = (6 - 2) * 180 / 6 = 120 degrees
Given that one of the interior angles of the regular polygon is equal to (9/8) times the interior angle of a hexagon, we can write:
Interior angle of polygon = (9/8) * 120 degrees = 135 degrees
Now that we know the interior angle of the polygon, we can use it to find the number of sides using the formula:
Number of sides = 360 degrees / Interior angle of polygon
Number of sides = 360 degrees / 135 degrees = 2.6667
Since the number of sides must be a whole number for a polygon, we need to round up to the nearest whole number. Therefore, the regular polygon has 3 sides.
However, a polygon with 3 sides is not possible. In geometry, a polygon with 3 sides is called a triangle. Therefore, there must be a mistake in the given information, and it is not possible to determine the length of the interior sides of the polygons.
interior angles of a hexagon = 180(4)/6 = 120°
let the number of side of the polygon be n
180(n-2)/n = (9/8)(120)
180n - 360 = 135n
45n = 360
n = 8
Your question of " Then the interior side of the polygon is ....? " makes no sense
(notice my caps lock is not stuck like yours)
there are 2 possibilities -
1. you don't know English and just showing off with the little knowledge you have
2. all of the question is correct . He might be a rich person not like you typing on a mobile phone . He must be typing on the laptop and no one has this much time to see the caps lock is on or not
thank you
don't judge others