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.