SAT Question 3828f53d: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice A is correct. Given that lines $m$ and $n$ are parallel, the angle marked $130^{\circ }$ must be supplementary to the leftmost angle marked $a^{\circ }$ because they are same-side interior angles. Therefore, $130^{\circ }+a^{\circ }=180^{\circ }$, which yields $a=50^{\circ }$. Lines $l$ and $m$ intersect at a right angle, so lines $j$, $l$, and $m$ form a right triangle where the two acute angles are $a^{\circ }$ and $b^{\circ }$. The acute angles of a right triangle are complementary, so $a^{\circ }+b^{\circ }=90^{\circ }$, which yields $50^{\circ }+b^{\circ }=90^{\circ }$, and $b=40$.