SAT Question c41eb616: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice A is correct. It’s given that two lines intersect at exactly one point, forming two acute angles and two obtuse angles. When two lines intersect, opposite angles are congruent and adjacent angles are supplementary. It’s given that the measure of one of the angles is $(9x-140{)}^{\circ }$, so the measure of the opposite angle is $(9x-140{)}^{\circ }$, and the measure of each adjacent angle is $(180-(9x-140){)}^{\circ }$, or $(-9x+320{)}^{\circ }$. The possible sums of the measures of any two of the angles are $(9x-140{)}^{\circ }+(9x-140{)}^{\circ }$, or $(18x-280{)}^{\circ }$, $(-9x+320{)}^{\circ }+(-9x+320{)}^{\circ }$, or $(-18x+640{)}^{\circ }$, and $(9x-140{)}^{\circ }+(-9x+320{)}^{\circ }$, or $180{.}^{\circ }$ Of the given choices, only $(-18x+280{)}^{\circ }$ is not equivalent to any of these expressions and could not be the sum of the measures of any two of the angles.