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5

To find the number of obtuse angles in a regular pentagon we first need to find the sum of the interior angles in a pentagon. We can calculate the sum by using the formula:

##180^@(n-2)##

where:

##n## = number of sides the polygon has

##180^@(n-2)##

##=180^@((5)-2)##

##=180^@(3)##

##=540^@##

Since the pentagon is a regular polygon this means that all of the ##5## angles are equal to one another. We can find the degrees of one interior angle by doing the following:

##540^@-:5##

##=108^@##

Since an obtuse is any angle greater than ##90^@## but less than ##180^@## this means that ##108^@## must be an obtuse angle. Since there are ##5## ##108^@## angles in a pentagon then there are ##5## obtuse angles in a regular pentagon.

##:.## there are ##5## obtuse angles in a regular pentagon.

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