Question

Question #4cf20

Answer 1

As a basic acute angle (in degrees) `x~~10.25^circ`

Explanation:

[I have assumed that the question was presented with the argument expressed in degrees].

Using a calculator to determine the arctangent of `(-1.57)` as a basic angle:
`arctan(tan(2x-78^circ))=arctan(-1.57)`
`color(white)("xxxxxxxxxxx")2x-78^circ~~-57.5052...^circ`

Then solving for `x` by adding `78^circ` to both sides
`color(white)("XXX")2x~~20.4948^circ`
and dividing by `2`
`color(white)("XXX")x~~10.25^circ`