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)180(n2)

where:
nn = number of sides the polygon has

180^@(n-2)180(n2)
=180^@((5)-2)=180((5)2)
=180^@(3)=180(3)
=540^@=540

Since the pentagon is a regular polygon, this means that all of the 55 angles are equal to one another. We can find the degrees of one interior angle by doing the following:

540^@-:5540÷5
=108^@=108

Since an obtuse is any angle greater than 90^@90 but less than 180^@180, this means that 108^@108 must be an obtuse angle. Since there are 55 108^@108 angles in a pentagon, then there are 55 obtuse angles in a regular pentagon.

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