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EXPLANATION:
We know that
Each interior angle of a regular polygon of n sides is {(n-2)/n}×180°
Given,
Each interior angle of the regular polygon = 160°
⇛{(n-2)/n}×180° = 160°
⇛(n-2)/n = 160°/180°
⇛(n-2)/n = 8/9
Now, applying cross multiplication then, we get
⇛9(n-2) = 8n
⇛9n-18 = 8n
⇛9n -8n = 12
⇛n=12
The number of sides in the given regular polygon = 12
One third of 12 = 12/3 = 4
Now,
We have ,n = 4
Each interior angle of a regular polygon of n sides is {(n-2)/n}×180°
⇛{(4-2)/4}×180°
⇛(2/4)×180°
⇛180°/2
⇛90°
Each interior angle = 90°
Answer: •The number of sides in the given regular polygon =12 •The interior angle of one third of the number of sides of the first polygon is 90°.
The polygon with 160 degree as the interior angle has 18 sides.
The interior angle of a regular polygon with one-third of side of the first polygon is 120 degrees
Regular polygons are polygons that are equiangular. They have the same angles. Therefore,
Interior angle of polygon = (n - 2 )180 / n
Therefore,
160n = 180n - 360
360 = 180n - 160n
n = 360 / 20
n = 18
Therefore, a polygon with 160 degree as the interior angle has 18 sides.
The interior angle of a regular polygon with one-third number of sides as the first polygon is as follows:
This means the polygon has 6 sides.
Interior angle = (6 - 2)180 / 6
interior angle = 4 × 180 / 6
interior angle = 720 / 6
interior angle = 120°
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