Question

How many obtuse angles in a regular pentagon?

Answer 1

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.