Question

algebra find m∠deg ar (18x - 9)° (4x + 13)°

Explanation:

Step1: Set up an equation

Since $\angle DEG$ and $\angle GEF$ are supplementary (they form a straight - line), we have $(18x - 9)+(4x + 13)=180$.

Step2: Combine like terms

$18x+4x-9 + 13=180$, which simplifies to $22x+4 = 180$.

Step3: Isolate the variable term

Subtract 4 from both sides: $22x=180 - 4$, so $22x=176$.

Step4: Solve for x

Divide both sides by 22: $x=\frac{176}{22}=8$.

Step5: Find $m\angle DEG$

Substitute $x = 8$ into the expression for $\angle DEG$: $m\angle DEG=18x-9=18\times8 - 9=144-9 = 135^{\circ}$.

Answer:

$m\angle DEG = 135^{\circ}$