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.

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°.