Question

Which of the following are measures of the angle shown? Select all that apply.

Answer 1

For convenion, the angles are measured from x-axis and counterclock wise, that is

Then, our angle measure 180 degrees (green arrow) + 30 degrees

$180+30=210$

Then, the answer is option D.

We also can measure the angle clockwise, but with negative sign, that is

that is, our angle measure -180 degrees plus 30 degrees, which is equal to -150 degrees. So, we must find an equivalent expression for -150 degrees. This can be obtained by substraction 360 degrees to our angle, which means one round to our scheme:

then, an equivalent answer is -510 degrees.

In summary, our angle can be represented as 210 degrees and -510 degrees.