Chapter 1.4, Problem 48PPS

a.

To determine

To construct the given figure.

Explanation of Solution

Given information:

Draw four lines, each with points A, B and C, draw line $\overrightarrow{BD}$ varying the placement of D

Construction:

Figure 1:

  

  $\angle ABD=45°$ ,

  $\angle DBC=135°$

Figure 2:

  

  $\angle ABD=60°$ ,

  $\angle DBC=120°$

Figure 3:

  

  $\angle ABD=90°$ ,

  $\angle DBC=90°$

Figure 3:

  

  $\angle ABD=155°$ ,

  $\angle DBC=25°$

b.

To determine

To construct a table for each figure.

Explanation of Solution

Given information:

Figures.

Calculation:

Figure	$\angle ABD$	$\angle DBC$	$\angle ABD$+$\angle DBC$
1	$45°$	$135°$	$180°$
2	$60°$	$120°$	$180°$
3	$90°$	$90°$	$180°$
4	$155°$	$25°$	$180°$

c.

To determine

To explain the given problem

Answer to Problem 48PPS

Sum is 180

Explanation of Solution

Given information:

Sum of $\angle ABD$ and $\angle DBC$

Evaluation:

Concluding from the figure.

The sum of $\angle ABD$ and $\angle DBC$ is always $180°$ because $\overrightarrow{AC}$ is a straight line.

d.

To determine

To write an equation.

Answer to Problem 48PPS

  $x+y=180°$

Explanation of Solution

Given information:

  $x$ is measure of $\angle ABD$ and $y$ is measure of $\angle DBC$

Evaluation:

The angles are supplementary angles. Hence, the required will be,

  $x+y=180°$