Each interior angle of a regular polygon is 174⁰. What is the number of sides of the polygon
Answers
Answer:
ae=6 degrees which is a enterior angle
Step-by-step explanation:
The measure of each interior angle A%5Bi%5D of a regular polygon of n sides can be expressed by:
A%5Bi%5D+=+%28n-2%29%2A180%2Fn
In this problem, A%5Bi%5D+=+174degrees, so we substitute...
174+=+%28n-2%29%2A180%2Fn Multiply both sides by n and simplify.
174n+=+180n-360 Add 360 to both sides.
174n%2B360+=+180n Subtract 174n from both sides.
360+=+6n Finally, divide both sides by 6.
60+=+n
The polygon has 60 sides.
The exterior angle A%5Be%5D is supplement of the interior angle, so...
A%5Be%5D+=+180-A%5Bi%5D
A%5Be%5D+=+180-174
A%5Be%5D+=+6degrees
Answer:
60 Sides
Step-by-step explanation:
A quick way to do is is:
174n⁰ (Interior angle)= 180n-360
It's like algebra, we are moving the numbers that have n on one side-so we do 174n-180n=-360
174-180=-6n
so -6n=-360
-360 divided by -6= 60
So the answer is 60 sides :)