To determine the reference angle for an angle [tex]\( x \)[/tex] measuring [tex]\( 150^\circ \)[/tex], we need to understand the concept of reference angles. A reference angle is the smallest angle that the terminal side of the given angle makes with the x-axis.
Since [tex]\( x = 150^\circ \)[/tex] is situated in the second quadrant (90° to 180°), the reference angle can be found using the following rule:
For an angle between 90° and 180°, the reference angle is [tex]\( 180^\circ - x \)[/tex].
Now, let's find the reference angle for [tex]\( x = 150^\circ \)[/tex]:
[tex]\[ \text{Reference angle} = 180^\circ - x \][/tex]
[tex]\[ \text{Reference angle} = 180^\circ - 150^\circ \][/tex]
[tex]\[ \text{Reference angle} = 30^\circ \][/tex]
Hence, the expression that can be used to determine the reference angle for an angle measuring [tex]\( 150^\circ \)[/tex] is:
[tex]\[ 180^\circ - x \][/tex]
So, the correct choice is:
[tex]\[ 180^{\circ}-x \][/tex]
