Find the measure of $\angle RST$. (Hint: Draw a line through S parallel to $\overline{RX}$and $\overline{TY}$.)

The measurement of angles that are positioned on alternate interior side is equal when the lines related to the angles are having a parallel relation.

Draw a line S that is having a parallel relation with existing parallel lines.

According to the obtained figure the lines XR and US are having a parallel relation and a separate line RS is travelling through them so according to the method the measurement of $\angle 1$and $\angle SRX$will be the same.

$\angle 1=\angle SRX=40°$

According to the obtained figure the lines YT and US are having a parallel relation and a separate line ST is travelling through them so according to the method the measurement of $\angle 2$and $\angle STY$will be the same.

$\angle 2=\angle STY=70°$

According to the obtained figure $\angle RST$is the addition of $\angle 1$and$\angle 2$ so determine the measurement of $\angle RST$.

$\angle RST=\angle 1+\angle 2$

$=40°+70°$

$=110°$