In a regular polygon the interior angles are 36 degrees greater than the exterior angles. How many sides does this polygon have?

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The interior and exterior angles are supplementary ones, thus the sum of their measures is `180` degrees. So if we denote an exterior angle measure as `x,` then the interior measure is `180-x.` It is also given that "the interior angles are 36 degrees greater than the exterior angles",

`180-x...

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Hello!

The interior and exterior angles are supplementary ones, thus the sum of their measures is `180` degrees. So if we denote an exterior angle measure as `x,` then the interior measure is `180-x.` It is also given that "the interior angles are 36 degrees greater than the exterior angles",

`180-x = 36+x,`

therefore `x=(180-36)/2=72` (degrees).

For a regular polygon with `n` angles (and `n` sides, of course), an exterior angle has the measure of `360/n.` So we have

`360/n=72,` or `n=360/72=5.`

The answer: this polygon has 5 sides.

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