Question

This jewelry box has the shape of a regular pentagon. It is packaged in a rectangular box as shown here. The box uses two pairs of congruent right triangles made of foam to fill its four corners. Find the measure of the foam angle marked.

Answer 1

72°

Explanation:

The measure of each interior angle of an regular n-gon is given by:

Each interior =
`((n-2)*180)/(n)`

So each interior of the pentagon will be
`((5-2)*180)/(5)\\=(3*180)/(5)\\=108`

Now we can see that the angle x is supplementary to interior angle of pentagon. So that means angle x and interior angle of pentagon add up to 180, so we can write:

108 + x = 180

x = 180 - 108 = 72

72 degrees is the right answer.