SAT Question 17912810: Lines, Angles, and Triangles answer and explanation with Desmos solution

In the figure, lines $q$, $r$, and $s$ form a triangle. One interior angle of this triangle is vertical to the angle marked $a^{\circ }$; therefore, the interior angle also has measure $a^{\circ }$. It's given that $a=43$. Therefore, the interior angle of the triangle has measure $43^{\circ }$. A second interior angle of the triangle forms a straight line, $q$, with the angle marked $b^{\circ }$. Therefore, the sum of the measures of these two angles is $180^{\circ }$. It's given that $b=122$. Therefore, the angle marked $b^{\circ }$ has measure $122^{\circ }$ and the second interior angle of the triangle has measure ${\left(180-122\right)}^{\circ }$, or $58^{\circ }$. The sum of the interior angles of a triangle is $180^{\circ }$. Therefore, the measure of the third interior angle of the triangle is ${\left(180-43-58\right)}^{\circ }$, or $79^{\circ }$. It's given that parallel lines $q$ and $t$ are intersected by line $r$. It follows that the triangle's interior angle with measure $79^{\circ }$ is congruent to the same side interior angle between lines $q$ and $t$ formed by lines $t$ and $r$. Since this angle is supplementary to the two angles marked $w^{\circ }$, the sum of $79^{\circ }$, $w^{\circ }$, and $w^{\circ }$ is $180^{\circ }$. It follows that $79+w+w=180$, or $79+2w=180$. Subtracting $79$ from both sides of this equation yields $2w=101$. Dividing both sides of this equation by $2$ yields $w=\frac{101}{2}$. Note that 101/2, 50.5, and 50.50 are examples of ways to enter a correct answer.