Chapter 3.5, Problem 1ECYP

To determine

To state the postulate or theorem justify the answer.

  $m\angle 8+m\angle 13={180}^{°}$

Answer to Problem 1ECYP

Theorem of co-interior angles

When two lines are cut by a transversal and sum of co-interior angles is ${180}^{°}$ , then lines are parallel.

Explanation of Solution

Given information:

Figure

  $m\angle 8+m\angle 13={180}^{°}$

Figure

Theorem of co-interior angles

When two lines are cut by a transversal and sum of co-interior angles is ${180}^{°}$ , then lines are parallel.

In figure parallel lines are

  $l\left|\right|m$

From above theorem

Corresponding angle $\angle 8$ on transversal b of line l and angle $\angle 13$ on transversal b of line m are co-interior angles.

And total of co-interior angles is ${180}^{°}$

Then

  $m\angle 8+m\angle 13={180}^{°}$

Hence, angles are co-interior angles.