sat-dog

The correct answer is $\frac{101}{2}$. In the figure, lines $q$, $r$, and $s$ form a triangle. One interior angle of this triangle is vertical to the angle marked $a°$; therefore, the interior angle also has measure $a°$. It's given that $a=43$. Therefore, the interior angle of the triangle has measure $43°$. A second interior angle of the triangle forms a straight line, $q$, with the angle marked $b°$. Therefore, the sum of the measures of these two angles is $180°$. It's given that $b=122$. Therefore, the angle marked $b°$ has measure $122°$ and the second interior angle of the triangle has measure $\left(180-122\right)°$, or $58°$. The sum of the interior angles of a triangle is $180°$. Therefore, the measure of the third interior angle of the triangle is $\left(180-43-58\right)°$, or $79°$. It's given that parallel lines $q$ and $t$ are intersected by line $r$. It follows that the triangle's interior angle with measure $79°$ 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 $w°$, the sum of $79°$, $w°$, and $w°$ is $180°$. 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 and 50.5 are examples of ways to enter a correct answer.