Chapter 3.3, Problem 29WE

To determine

To calculate: $x,y$

Answer to Problem 29WE

  $x=50°,y=20°$

Explanation of Solution

Given information:A figure is given in which two lines are parallel to each other

Calculation:

Consider the following figure.

  

First find the first equation.

  $DF\parallel BC$ (Given)

Take AB as a transversal.

  $\angle DAB=\angle ABC$ (Alternate interior angles are equal)

So,

Put $\angle DAB=5y°,\angle ABC=2x°$

That is

  $\begin{array}{l}5y°=2x°\\ \Rightarrow x°=\frac{5y°}{2}(i)\end{array}$

Now find the second equation.

  $DF\parallel BC$ (Given)

Take EC as transversal.

  $\angle EAD=\angle ACB$ (Pair of corresponding angles is equal)

Put $\angle EAD=30°,\angle ACB=(x-y)°$

So,

  $(x-y)°=30°(ii)$

Now solve equation $(i),(ii)$

Put $x°=\frac{5y°}{2}$ in $(x-y)°=30°$

  $\begin{array}{l}\frac{5y}{2}-y=30\\ \Rightarrow \frac{5y-2y}{2}=30\\ \Rightarrow 3y=60\\ \Rightarrow y=\frac{60}{3}=20°\end{array}$

Put $y=20°$ in (i)

  $x=\frac{5(20°)}{2}=50°$

Therefore,

  $x=50°,y=20°$