Chapter 3.2, Problem 13CE

To determine

To find: the $m\angle 1$ given that $m\angle 5=m\angle 6+20$ .

Answer to Problem 13CE

  $m\angle 1=100$

Explanation of Solution

Given:

The diagram:

Concept Used:

Postulate 10: If two parallel lines are cut by a transversal then the corresponding angles are congruent

Theorem 3-2: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

Vertically opposite angles are congruent.

Consider the given figure:

In this figure,

  $\angle 1\cong \angle 5$ (Corresponding angles)

Thus,

  $m\angle 5=m\angle 1$ ….. (1)

And,

  $m\angle 5+m\angle 6=180$ (Supplementary angles)

Substitute $m\angle 5=m\angle 6+20$ in above equation,

  $\begin{array}{c}m\angle 6+20+m\angle 6=180\\ 2m\angle 6=180-20\\ 2m\angle 6=160\\ m\angle 6=80\end{array}$

Now substitute $m\angle 6=80$ in $m\angle 5=m\angle 6+20$ ,

  $\begin{array}{c}m\angle 5=80+20\\ =100\end{array}$

Then, by equation (1),

  $m\angle 1=m\angle 5=100$