How many obtuse angles in a regular pentagon?

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.