Chapter 3.3, Problem 28WE

To determine

To calculate: measure of $\angle RST$

Answer to Problem 28WE

  $\angle RST=130°$

Explanation of Solution

Formula used: If lines are parallel then sum of interior angles is equal to $180°$

Calculation:

  

Draw a line through S parallel to RX and TY.

First find $\angle 1,\angle 2$

As $XR\parallel US$ and take $RS$ as a transversal,

  $\angle 1+110°=180°$

(if lines are parallel then sum of interior angles is $180°$ )

So,

  $\angle 1=180°-110°=70°$

As $YT\parallel US$ and take $ST$ as a transversal,

  $\angle 2+120°=180°$

(if lines are parallel then sum of interior angles is $180°$ )

So,

  $\angle 2=180°-120°=60°$

Now find $\angle RST$

  $\begin{array}{l}\angle RST=\angle 1+\angle 2\\ =70°+60°\\ =130°\end{array}$

Therefore,

  $\angle RST=130°$