Help please!!!!
<EFG and <GFH are a linear pair, m<EFG=2n+22, and m<GFH=4n+38. What are m<EFG and m<GFH?
a linear pair sums to 180º
(2n + 22) + (4n + 38) = 180
... solve for n , then substitute back to find m<EFG and m<GFH
180
To find the measures of <EFG and <GFH, we'll use the fact that angles forming a linear pair sum up to 180 degrees.
We are given that <EFG and <GFH are a linear pair, which means they are adjacent angles formed by two intersecting lines and therefore their measures add up to 180 degrees.
Let's set up an equation to represent this relationship:
m<EFG + m<GFH = 180
We are also given that m<EFG = 2n + 22 and m<GFH = 4n + 38.
Substitute these values into the equation:
(2n + 22) + (4n + 38) = 180
Now, combine like terms:
2n + 4n + 22 + 38 = 180
Simplify:
6n + 60 = 180
Next, isolate the variable term:
6n = 180 - 60
6n = 120
Finally, divide both sides by 6 to solve for n:
n = 120 / 6
n = 20
Now that we have the value of n, we can substitute it back into the expressions for m<EFG and m<GFH to find their measures:
m<EFG = 2n + 22 = 2(20) + 22 = 40 + 22 = 62 degrees
m<GFH = 4n + 38 = 4(20) + 38 = 80 + 38 = 118 degrees
Therefore, the measure of <EFG is 62 degrees, and the measure of <GFH is 118 degrees.