To determine the angle that is supplementary to an angle measuring [tex]\(165^{\circ}\)[/tex], we need to use the concept of supplementary angles. By definition, two angles are supplementary if the sum of their measures is [tex]\(180^{\circ}\)[/tex].
Given:
[tex]\[ \text{Given angle} = 165^{\circ} \][/tex]
Let [tex]\(x\)[/tex] be the measure of the supplementary angle. According to the definition of supplementary angles:
[tex]\[ 165^{\circ} + x = 180^{\circ} \][/tex]
To find [tex]\(x\)[/tex], we subtract [tex]\(165^{\circ}\)[/tex] from [tex]\(180^{\circ}\)[/tex]:
[tex]\[ x = 180^{\circ} - 165^{\circ} \][/tex]
[tex]\[ x = 15^{\circ} \][/tex]
Therefore, the angle supplementary to [tex]\(165^{\circ}\)[/tex] is [tex]\(15^{\circ}\)[/tex].
Among the given options, the correct answer is:
D. [tex]\(15^{\circ}\)[/tex]
