# How many obtuse angles in a regular pentagon?

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:

${180}^{\circ} \left(n - 2\right)$

where:
$n$ = number of sides the polygon has

${180}^{\circ} \left(n - 2\right)$
$= {180}^{\circ} \left(\left(5\right) - 2\right)$
$= {180}^{\circ} \left(3\right)$
$= {540}^{\circ}$

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:

${540}^{\circ} \div 5$
$= {108}^{\circ}$

Since an obtuse is any angle greater than ${90}^{\circ}$ but less than ${180}^{\circ}$, this means that ${108}^{\circ}$ must be an obtuse angle. Since there are $5$ ${108}^{\circ}$ angles in a pentagon, then there are $5$ obtuse angles in a regular pentagon.

$\therefore$, there are $5$ obtuse angles in a regular pentagon.