Chapter 2.8, Problem 2PSA

a

To determine

To calculate : The value of $\angle 2$ is to be calculated

Answer to Problem 2PSA

The value of $\angle 2$ is ${119}^0{28}^{\text{'}}$

Explanation of Solution

Given information : The following information can be predicted from the diagram

  $\angle 1={60}^0{32}^{\text{'}}$

  $\angle 1$ and $\angle 3$ are vertically opposite angles

  $\angle 2$ and $\angle 4$ are vertically opposite angles

Formula used : We will use the following formulas

Vertically opposite angles have same measurements

Supplementary angles add up to ${180}^0$

Calculation : We can see that $\angle 2$ is the supplementary angle for $\angle 1={60}^0{32}^{\text{'}}$

Hence, we can say that

  $\angle 2={180}^0-{60}^0{32}^{\text{'}}={119}^0{28}^{\text{'}}$

Hence, the desired value is calculated

b

To determine

To calculate : The value of $\angle 3$ is to be calculated

Answer to Problem 2PSA

The value of $\angle 3$ is ${60}^0{32}^{\text{'}}$

Explanation of Solution

Given information : The following information can be predicted from the diagram

  $\angle 1={60}^0{32}^{\text{'}}$

  $\angle 1$ and $\angle 3$ are vertically opposite angles

  $\angle 2$ and $\angle 4$ are vertically opposite angles

Formula used : We will use the following formulas

Vertically opposite angles have same measurements

Supplementary angles add up to ${180}^0$

Calculation : We can see that $\angle 3$ is the vertically opposite angle for $\angle 1={60}^0{32}^{\text{'}}$

Hence, we can say that

  $\angle 3={60}^0{32}^{\text{'}}$

Hence, the desired value is calculated

c

To determine

To calculate : The value of $\angle 4$ is to be calculated

Answer to Problem 2PSA

The value of $\angle 4$ is ${119}^0{28}^{\text{'}}$

Explanation of Solution

Given information : The following information can be predicted from the diagram

  $\angle 1={60}^0{32}^{\text{'}}$

  $\angle 1$ and $\angle 3$ are vertically opposite angles

  $\angle 2$ and $\angle 4$ are vertically opposite angles

Formula used : We will use the following formulas

Vertically opposite angles have same measurements

Supplementary angles add up to ${180}^0$

Calculation : We can see that $\angle 4$ is the supplementary angle for $\angle 1={60}^0{32}^{\text{'}}$

Hence, we can say that

  $\angle 4={180}^0-{60}^0{32}^{\text{'}}={119}^0{28}^{\text{'}}$

Hence, the desired value is calculated