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 $\mathbf{\angle }\mathit{R}\mathit{S}\mathit{T}\mathbf{=}\mathbf{130}\mathbf{°}$.

Step-by-step solution

Step 1. Determine the method that can be used

The sum of measurement of angles that are positioned on interior side is equal to $180°$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 write the measurement of $\angle 1$.

$\angle 1+110°=180°$

$\angle 1=180°-110°$

$=70°$

Step 4. Determine the value of

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 write the measurement of $\angle 2$.

$\angle 2+120°=180°$

$\angle 2=180°-120°$

$=60°$

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 $\angle RST$.

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

$=70°+60°$

$=130°$