# a regular polygon has an interior angle of 172 find the number of sides of this polygon ?

## a regular polygon has an interior angle of 172 find the number of sides of this polygon ? ### Questions and explanations:

Each interior angle if a regular polygon measures 172 degrees, how many sides does the polygon have?
The easiest way to solve this problem is to use the outer corners of the polygon. The sum of the exterior and interior angles is 180 degrees. Also, the sum of all exterior angles of a polygon

What is a 172 sided polygon called?
The name of a 172 sided polygon is ChiliHeptacontakaidigon.

What is 172-86?
258

What is 364 plus 172 equals?
364 + 172 = 536

What is 3 divided by 172?
0.0174

## Answers from some readers B. Math. (Hons.) Mathematics, The University of Newcastle (1981)

As you go around the perimeter of this polygon, each side represents a turn to the left (if you are going anticlockwise) or right (if you are going clockwise) of (180 – 172) deg. = 8 deg. A complete revolution represents a turn of 360 deg. So the number of sides = 360/8 = 45.

If each of the interior angles is 172 degrees, then each of the exterior angles is 8 degrees. Since the sum of the exterior angles of any polygon is 360 degrees, there are 360 / 8 = 45 exterior angles and 45 sides.

Ph.D. in Civil Engineering. Maths keeps one mentally active.

A regular polygon has an interior angle = 172 deg.

So each exterior angle of the regular polygon = 180–172 = 8 deg.

The number of sides of the regular polygon = 360/8 = 45.

## F.A.Q a regular polygon has an interior angle of 172 find the number of sides of this polygon

7740 degrees

### 2. Is it conceivable that the internal angles of a regular polygon might measure a total of 8 degrees?

No. If the angle on the inside measures 8 degrees, then each angle on the outside must measure 172 degrees. Since 360 is more than 172, the polygon must have around 2.1 sides. It is not feasible to have a fractional side.

### 3. How many sides does a regular polygon have if one of its angles measures 172 degrees?

If one of the inside angles is measured at 172 degrees, then the equivalent outside angle will be measured at 180 degrees minus 172 degrees, which equals 8 degrees. The number of sides is equal to 45 since 360 minus 8 equals 45.

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