Question

EFG and GFH are a linear pair, EFG=2n+17 and GFH=4n+19. What are EFG and GFH?

a) EFG = 19, GFH = 35
b) EFG = 17, GFH = 23
c) EFG = 21, GFH = 29
d) EFG = 23, GFH = 31

Answer 1

After solving the equations EFG = 2n + 17 and GFH = 4n + 19 with the condition that they sum to 180 degrees for a linear pair, we find that EFG = 65 and GFH = 115. None of the given options match these results, indicating a possible error in the question or the options provided.

Step-by-step explanation:

We have a pair of linear angles EFG and GFH with the given equations EFG = 2n + 17 and GFH = 4n + 19. Since they form a linear pair, their sum must be equal to 180 degrees. Therefore, we can set up an equation:

2n + 17 + 4n + 19 = 180

Solving this equation for n, we get:

6n + 36 = 180

6n = 144

n = 24

Now we substitute the value of n back into the expressions for EFG and GFH:

EFG = 2(24) + 17 = 48 + 17 = 65

GFH = 4(24) + 19 = 96 + 19 = 115

However, none of the options matches these values, indicating that there might have been a typo in the question or the provided answer choices.