Chapter 1.5, Problem 48PPS

a.

To determine

To construct the given figure.

Explanation of Solution

Given information:

Draw three intersecting lines.

Calculation:

Figure 1:

  

Figure 2:

  

Figure 3:

  

b.

To determine

To construct a table for each figure.

Explanation of Solution

Given information:

The figures

Construction:

Figure	$m\angle 1$	$m\angle 2$	$m\angle 3$	$m\angle 1$+ $m\angle 2$+ $m\angle 3$
1	$60°$	$60°$	$60°$	$180°$
2	$40°$	$70°$	$70°$	$180°$
3	$80°$	$60°$	$40°$	$180°$

c.

To determine

To calculate $m\angle 4,m\angle 5,m\angle 6$

Answer to Problem 48PPS

  $\angle 1=\angle 4,\angle 2=\angle 5,\angle 3=\angle 6$

Explanation of Solution

Given information:

Value of $m\angle 1,m\angle 2$ and $m\angle 3$

Evaluation:

  $\angle 1$ is vertically opposite to $\angle 4$ , $\angle 2$ is vertically opposite to $\angle 5$ and $\angle 3$ is vertically opposite to $\angle 6$ .

Therefore,

  $\angle 1=\angle 4,\angle 2=\angle 5,\angle 3=\angle 6$

d.

To determine

To write an equation.

Answer to Problem 48PPS

  $\angle 4+\angle 5+\angle 6=180$

Explanation of Solution

Given information:

An equation that relates $\angle 1+\angle 2+\angle 3$ to $\angle 4+\angle 5+\angle 6$

Evaluation:

The will be:

  $\angle 1+\angle 2+\angle 3=\angle 4+\angle 5+\angle 6$

Or

  $\angle 1+\angle 2+\angle 3+\angle 4+\angle 5+\angle 6=360$

And,

  $\angle 4+\angle 5+\angle 6=180$