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2 years ago

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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.
⚠️Fake answer not allow. ✔️Best answer will be marked as brilliant.

2 answers:

Karolina [17]2 years ago

4 0

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

<h3 />

<h3>What are regular Polygon?</h3>

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°

learn more on polygon here: brainly.com/question/24393300?referrer=searchResults

IrinaK [193]2 years ago

4 0

<u>EXPLANATION</u><u>:</u>

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°

<u>Answer</u><u>:</u> •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°.

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