Answer: ∠DFG = 53 degrees, ∠JKL = 37 degrees.
Step-by-step explanation:
If ∠DFG and ∠JKL are complementary angles, it means that the sum of their measures is equal to 90 degrees. In other words:
m∠DFG + m∠JKL = 90 degrees
Now, we are given that:
m∠DFG = x + 7
m∠JKL = x - 9
We can substitute these values into the equation for complementary angles:
(x + 7) + (x - 9) = 90
Now, let's solve for x:
Combine like terms:
2x - 2 = 90
Add 2 to both sides to isolate 2x:
2x = 92
Now, divide by 2 to find the value of x:
x = 92 / 2
x = 46
Now that we've found the value of x, we can use it to find the measures of ∠DFG and ∠JKL:
m∠DFG = x + 7 = 46 + 7 = 53 degrees
m∠JKL = x - 9 = 46 - 9 = 37 degrees
So, the measure of ∠DFG is 53 degrees, and the measure of ∠JKL is 37 degrees.