Question

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

Short answer

The obtained conclusion is that $\mathbf{\angle }\mathit{R}\mathit{S}\mathit{T}\mathbf{=}\mathbf{110}\mathbf{°}$.

Step-by-step solution

Step 1. Determine the method that can be used

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.

Step 2. Recreate the provided figure

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

Step 3. Determine the value of angle 1

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.

$\angle 1=\angle SRX=40°$

Step 4. Determine the value of angle 2

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.

$\angle 2=\angle STY=70°$

Step 5. Determine the value of angle RST

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

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

$=40°+70°$

$=110°$