Chapter 3.5, Problem 43HP

To determine

Describe a situation in which two parallel lines are cut by a transversal and a pair of consecutive interior angles are both supplementary and congruent.

Answer to Problem 43HP

Both the consecutive interior angles should be right angled to be both supplementary and congruent.

Explanation of Solution

Calculation :

Let the measures of two consecutive interior angles which are both supplementary and congruent be x and y .

Since they are supplementary , so :

  $x+y=180°$ ……........(1)

Since they are congruent , so :

  $x=y$

Substitute in (1) :

  $\begin{array}{l}x+y=180°\\ \Rightarrow x+x=180°\\ \Rightarrow 2x=180°\\ \Rightarrow x=\frac{180°}{2}\mathrm{............}[\text{divide each side by 2]}\\ \Rightarrow x=90°\\ \Rightarrow y=90°\end{array}$

So, both the consecutive interior angles should be right angled to be both supplementary and congruent.