Question

Find this angle?

Answer 1

Use these facts:
The interior angle of a regular pentagon is `108^@`
The lines of symmetry bisect the angles and are perpendicular to the opposite side.

Explanation:

Let O be the point where the two lines intersect.

The facts allow us to find the angles for the triangle formed by AOC:

`54^@` because the `108^@` angle is bisected

`90^@`, because the line of symmetry is perpendicular to that side.

This gives us the `angle AOC = 180^@-54^@-90^@ = 36^@`

`angle AOC` is supplemental to `angle x`:

`angle x = 180^@-36^@`

`angle x = 144^@`