Question

1. select the correct set - up to the problem
2. solve for x
3. find the measures of the angles (substitute the x)

angle dfg and angle jkl are supplementary angles. m∠dfg = x + 5 and m∠jkl = x - 9.

1. set equation: x + 5 + x-
2. solve for x = 92
3. measure of angle dfg = select

select
15
83
38
52
97

Explanation:

Step1: Set up the equation

Since supplementary angles add up to 180 degrees, we set up the equation $(x + 5)+(x - 9)=180$.
Combining like - terms, we get $2x-4 = 180$.

Step2: Solve for x

Add 4 to both sides of the equation: $2x-4 + 4=180 + 4$, which simplifies to $2x=184$.
Divide both sides by 2: $\frac{2x}{2}=\frac{184}{2}$, so $x = 92$.

Step3: Find the measure of angle DFG

Substitute $x = 92$ into the expression for $\angle DFG$. $\angle DFG=x + 5$, so $\angle DFG=92+5=97$.

Answer:

1. Set equation: $x + 5+x - 9=180$
2. Solve for $x$: $92$
3. Measure of angle DFG: $97$