Chapter 3.6, Problem 6ST2

To determine

Tocalculate:values of $y,z$

Answer to Problem 6ST2

  $y=50°,z=60°$

Explanation of Solution

Formula used: If a transversal intersects two parallel lines then each pair of alternate interior angles are equal.

Calculation:

Consider the following figure.

  

First find value of $z$

  $AB\parallel CD$

Take AD as a transversal

So,

  $\angle ODC+110°=180°$

(if a transversal intersects two parallel lines then sum of each pair of interior angles is equal to $180°$ )

  $\angle ODC=180°-110°=70°$

In $\Delta OCD$ ,

  $\angle ODC+\angle OCD+\angle COD=180°$

(according to angle sum property of a triangle, sum of angles is equal to $180°$ )

Put $\angle ODC=70°,\angle OCD=50°$

So,

  $\begin{array}{l}70°+50°+\angle COD=180°\\ \Rightarrow 120°+\angle COD=180°\\ \Rightarrow \angle COD=180°-120°\\ \Rightarrow \angle COD=60°\\ \Rightarrow z=60°\end{array}$

Now find value of $y$

Now $AB\parallel CD$

Take BC as a transversal

  $\angle ABO=\angle OCD$

(If a transversal intersects two parallel lines then each pair of alternate interior angles are equal)

Put $\angle ABO=y,\angle OCD=50°$

So,

  $y=50°$

Therefore,

  $y=50°,z=60°$