Chapter 2.7, Problem 13PSB

a

To determine

To calculate : The measurement of the angle $\angle HFK$ is to be calculated

Answer to Problem 13PSB

The value of $\angle HFK={180}^0-(x+y)$

Explanation of Solution

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

  $\angle HFE=x$

  $\angle KFG=y$

Formula used : The following formula has been used

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

Calculation : We can see that x and y together form supplementary angles for $\angle HFK$

Hence, we can say that

  $\angle HFK={180}^0-(x+y)$

Thus, the desired value is obtained

b

To determine

To calculate : The measurement of the angle $\angle EFK$ is to be calculated

Answer to Problem 13PSB

The value of $\angle EFK={180}^0-y$

Explanation of Solution

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

  $\angle HFE=x$

  $\angle KFG=y$

Formula used : The following formula has been used

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

Calculation : We can see that x and y together form supplementary angles for $\angle HFK$

Hence, we can say that

  $\angle HFK={180}^0-(x+y)$

Now, we also know that

  $\angle HFK+x=\angle EFK$

Now, substituting the value of $\angle HFK$ from the previous part, we can say that

  $\angle EFK={180}^0-y$

Thus, the desired value is obtained

c

To determine

To calculate : The measurement of the angle $\angle HFG$ is to be calculated

Answer to Problem 13PSB

The value of $\angle HFG={180}^0-x$

Explanation of Solution

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

  $\angle HFE=x$

  $\angle KFG=y$

Formula used : The following formula has been used

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

Calculation : We can see that $\angle HFG$ is supplementary angle to $\angle HFE=x$

Hence, we can say that

  $\angle HFG={180}^0-x$

Thus, the desired value is obtained