<EFG and <GFH are a linear​ pair, m<EFG=2n+22​, and m<GFH=4n+38. What are m<EFG and m<GFH?
To find the measures of angles <EFG and <GFH, we will use the given information that <EFG and <GFH form a linear pair. In a linear pair, the angles are adjacent and their measures add up to 180 degrees.
Let's set up an equation based on the given information:
m<EFG + m<GFH = 180
According to the problem, m<EFG = 2n + 22 and m<GFH = 4n + 38. Substitute these values into the equation:
(2n + 22) + (4n + 38) = 180
Simplify the equation:
6n + 60 = 180
Subtract 60 from both sides:
6n = 120
Divide both sides by 6:
n = 20
Now, substitute the value of n back into the equations for m<EFG and m<GFH:
m<EFG = 2(20) + 22 = 40 + 22 = 62
m<GFH = 4(20) + 38 = 80 + 38 = 118
Therefore, m<EFG = 62 and m<GFH = 118.