Question

Each interior angel of a regular polygon is 160°. How many sides does it have? Find the interior angel of a regular polygon with one-third number of sides as the first polygon.
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Answer 1

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

What are regular Polygon?

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:

• 1 / 3 × 18 = 6

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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Answer 2

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°.