How many obtuse angles in a regular pentagon?

1 Answer
Nov 27, 2015

5

Explanation:

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.