Chapter 3.2, Problem 6WE

To determine

To find: $m\angle 12$ and $m\angle 6$ if $m\angle 7=x$ .

Answer to Problem 6WE

  $m\angle 12=x$

  $m\angle 6=180-x$

Explanation of Solution

Given:

The diagram:

Concept Used:

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.

Consider the given figure:

Now, lines $c\parallel d$ and b is a transversal, so by theorem 3-2,

  $\angle 12\cong \angle 7$ (Corresponding angles)

That is,

  $m\angle 12=m\angle 7=x$

Similarly, lines $a\parallel b$ and c is a transversal, so by theorem 3-3, $\angle 6$ and $\angle 7$ are supplementary, that is,

  $\begin{array}{c}m\angle 6+m\angle 7=180\\ m\angle 6+x=180\\ m\angle 6=180-x\end{array}$