SAT Question 2d2cb85e: Lines, Angles, and Triangles answer and explanation with Desmos solution

In the figure shown, the sum of the measures of angle $UVS$ and angle $RVS$ is $180^{\circ }$. It's given that the measure of angle $RVS$ is $41^{\circ }$. Therefore, the measure of angle $UVS$ is ${\left(180-41\right)}^{\circ }$, or $139^{\circ }$. The sum of the measures of the interior angles of a triangle is $180^{\circ }$. In triangle $UVS$, the measure of angle $UVS$ is $139^{\circ }$ and it's given that the measure of angle $VST$ is $29^{\circ }$. Thus, the measure of angle $VUS$ is ${\left(180-139-29\right)}^{\circ }$, or $12^{\circ }$. It's given that $RT=TU$. Therefore, triangle $TUR$ is an isosceles triangle and the measure of $VUS$ is equal to the measure of angle $TRU$. In triangle $TUR$, the measure of angle $VUS$ is $12^{\circ }$ and the measure of angle $TRU$ is $12^{\circ }$. Thus, the measure of angle $UTR$ is ${\left(180-12-12\right)}^{\circ }$, or $156^{\circ }$. The figure shows that the measure of angle $UTR$ is $x^{\circ }$, so the value of $x$ is $156$.