Each interior angle of a regular polygon is equal to 172 degrees. Determine the number of sides of the polygon. Explain?

Question

Wyatt Anderson · Accepted Answer

#45# sides

A regular polygon with #n# sides has a total of #(n-2)180^o# internal degrees. This can be understood as the number of triangles in which the polygon can be decomposed. A regular polygon with an interior angle of #172^o# has a total of #n 172^o#. So we have #n 172 = (n-2)180#. Solving for #n# we have #n = 45#

James Atkins · Answer

undefined To determine the number of sides of the polygon, we can use the formula for calculating the sum of interior angles of a polygon, which is given by $ (n - 2) \times 180^\circ $, where $ n $ is the number of sides of the polygon.

Given that each interior angle of the polygon is $ 172^\circ $, we can set up the equation:

$$ 172^\circ \times n = (n - 2) \times 180^\circ $$

Solving for $ n $:

$$ 172^\circ \times n = 180^\circ \times n - 360^\circ $$

$$ 360^\circ = 180^\circ \times n - 172^\circ \times n $$

$$ 360^\circ = (180^\circ - 172^\circ) \times n $$

$$ 360^\circ = 8^\circ \times n $$

$$ n = \frac{360^\circ}{8^\circ} $$

$$ n = 45 $$

So, the polygon has 45 sides.