Chapter 4.2, Problem 42PPS

a.

To determine

To calculate:

The measure of angle $\mathrm{m}\angle 1$ and $\mathrm{m}\angle 2$ .

Answer to Problem 42PPS

The measure of angle $\mathrm{m}\angle 1$ and $\mathrm{m}\angle 2$ is $141°$ and $139°$ respectively.

Explanation of Solution

Given information:

  

Calculation:

The angle measurement value of $\mathrm{m}\angle 1$ is calculated by using the exterior angle theorem:

  $\begin{array}{l}\mathrm{m}\angle 1=70+71\\ \mathrm{m}\angle 1=141°\end{array}$

Use the sum of angel of triangle is $180°$ :

  $\begin{array}{l}70°+71°+\mathrm{m}\angle 2=180°\\ \mathrm{m}\angle 2=180°-141°\\ \mathrm{m}\angle 2=139°\end{array}$

b.

To determine

To explain:

The changes occurs in measure of angle $\mathrm{m}\angle 1$ .

Answer to Problem 42PPS

Angle measurement value of $\mathrm{m}\angle 1$ would get larger .

Explanation of Solution

From sub-part (a):

The angle measurement value of $\mathrm{m}\angle 1$ and $\mathrm{m}\angle 2$ are calculated as:

  $\begin{array}{l}\mathrm{m}\angle 1=141°\\ \mathrm{m}\angle 2=139°\end{array}$

As per problem statement:

If the support for the hood were shorter than the one shown in the given diagram then angle measurement value of $\mathrm{m}\angle 1$ would get larger because the hood would get closer to the triangle’s leg which is along the car’s fender.

c.

To determine

To explain:

The changes occurs in measure of angle $\mathrm{m}\angle 2$ .

Answer to Problem 42PPS

Angle measurement value of $\mathrm{m}\angle 2$ would get smaller.

Explanation of Solution

From sub-part (a):

The angle measurement value of $\mathrm{m}\angle 1$ and $\mathrm{m}\angle 2$ are calculated as:

  $\begin{array}{l}\mathrm{m}\angle 1=141°\\ \mathrm{m}\angle 2=139°\end{array}$

As per problem statement:

If the support for the hood were shorter than the one shown in the given diagram then angle measurement value of $\mathrm{m}\angle 2$ would get smaller because the hood would get far from the triangle’s leg and $\mathrm{m}\angle 1$ would get larger also which implies that these two angles are in the linear pair.