SAT Question 3e4e2ab0: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice A is correct. It’s given that $AE$ intersects $DB$ at point $C$ and that $AB$ is parallel to $DE$, creating triangles $ABC$ and $CDE$. Since $AB$ is parallel to $DE$, angles $BAC$ and $DEC$ are opposite interior angles and are congruent. It follows that the measure of angle $DEC$ is $y^{\circ }$. This means the three interior angles of triangle $CDE$ have measures of $x^{\circ }$, $z^{\circ }$, and $y^{\circ }$, respectively. It’s given that $x=63$ and $y=2x-47$. Substituting $63$ for $x$ in the equation $y=2x-47$ yields $y=2(63)-47$, or $y=79$. Therefore, the three interior angles of triangle $CDE$ have measures $63^{\circ }$, $z^{\circ }$, and $79^{\circ }$, respectively. The sum of the interior angles of a triangle is $180^{\circ }$. Therefore, $63+z+79=180$, or $z+142=180$. Subtracting $142$ from both sides of this equation yields $z=38$. Therefore, the value of $z$ is $38$.