Chapter 3.5, Problem 4CYU

To determine

To state the postulate or theorem justify the answer.

  $m\angle 6+m\angle 8={180}^{°}$

Answer to Problem 4CYU

Co-interior angles theorem.

Explanation of Solution

Given information:

Figure

  $m\angle 6+m\angle 8={180}^{°}$

Figure

In figure parallel lines are

  $a\left|\right|b$

And $l\left|\right|m$

Co-interior angle theorem

When two lines are parallel cut by a transversal and angles lie between lines at same side. then angle formed between lines are co-interior angles.And sum of co-interior angles is ${180}^o$ .

From above theorem

Then angle $\angle 6$ of line l on transversal k and angle $\angle 8$ of line m on transversal k are co-interior angles.

Then

  $m\angle 6+m\angle 8={180}^{°}$

Hence, $\angle 6$ and $\angle 8$ co-interior angles.