Question

Find the measure of the angle below?

Answer 1

`255^@`

Explanation:

We can interpret our angle as two parts:

`a.` The `75^@` angle

`b.` The angle around the `x`-axis

The angle we're looking for will be given by `a+b`. So what's `b`?

Well, we notice the angle looks reminiscent of a semicircle, which we know has a measure of `180^@`, so this is our `b`.

This makes intuitive sense too:

If we go from the negative `x` axis to the positive `y` axis, we moved `90^@`. If we go from there to the positive `x` axis, we moved another `90^@`. We traveled `180^@`.

Thus, the measure of this angle will be

`75+180`

`=>255^@`

Hope this helps!