Chapter 3.2, Problem 4WE

To determine

To name: all angles supplementary to $\angle 2$ .

Answer to Problem 4WE

The angles supplementary to $\angle 2$ are $\angle 1,\angle 3,\angle 6,\angle 8,\angle 9,\angle 11,\angle 14$ and $\angle 16$ .

Explanation of Solution

Given information:

Assume that $a\parallel b$ and $c\parallel d$ .

Calculation:

Refer to the figure provided in the text book.

Consider that “if $a\parallel b$ and $c\parallel d$ ” then

To find the angles that is supplementary to $\angle 2$ .

Therefore, $a$ and $b$ is as traversal for $c\parallel d$ and, $c$ and $d$ are traversal for $a\parallel b$ .

Use basically two postulates:

“If two lines are parallel to each other cut by a traversal then same side angles are supplementary”.

$\angle 2\text{and}\angle 1$ Supplementary angles.

$\angle 2\text{and}\angle 3$ Supplementary angles.

$\angle 2\text{and}\angle 6$ Supplementary angles.

Check that $\angle 2=\angle 10$ and, $\angle 10$ and $\angle 14$ are supplementary. So, angle $\angle 2$ and $\angle 14$ are supplementary.

Again, $\angle 1=\angle 9$ and, $\angle 2\text{and}\angle 1$ Supplementary angles. So, $\angle 2$ and $\angle 9$ are also supplementary.

Now, $\angle 2=\angle 7$ and, $\angle 7$ and $\angle 8$ are supplementary. So, angle $\angle 2$ and $\angle 8$ are supplementary.

Observe that $\angle 2=\angle 5$ , $\angle 5=\angle 13$ and $\angle 15=\angle 13$ . So, $\angle 2=\angle 15$ . Now, check that $\angle 15$ is supplementary to angles $\angle 11$ and $\angle 16$ . So, $\angle 2$ is also supplementary to angles $\angle 11$ and $\angle 16$ .

Therefore, the angles supplementary to $\angle 2$ are $\angle 1,\angle 3,\angle 6,\angle 8,\angle 9,\angle 11,\angle 14$ and $\angle 16$ .