Chapter 3.3, Problem 27WE

To determine

To calculate: measure of $\angle RST$

Answer to Problem 27WE

  $\angle RST=110°$

Explanation of Solution

Formula used: If lines are parallel then alternate interior angles are equal.

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,

  $\angle 1=\angle SRX=40°$

(if lines are parallel then alternate interior angles are equal)

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

  $\angle 2=\angle STY=70°$

(if lines are parallel then alternate interior angles are equal)

Now find $\angle RST$

  $\begin{array}{l}\angle RST=\angle 1+\angle 2\\ =40°+70°\\ =110°\end{array}$

Therefore,

  $\angle RST=110°$