Question

algebra find m∠deg and m∠gef. 17. (18x - 9)° (4x + 13)° d e f g 18.

Explanation:

Step1: Set up equation

Since $\angle DEG$ and $\angle GEF$ are a linear - pair, their sum is $180^{\circ}$. So, $(18x - 9)+(4x + 13)=180$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $18x+4x-9 + 13=180$, which simplifies to $22x+4 = 180$.

Step3: Solve for $x$

Subtract 4 from both sides: $22x=180 - 4=176$. Then divide both sides by 22: $x=\frac{176}{22}=8$.

Step4: Find $m\angle DEG$

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

Step5: Find $m\angle GEF$

Substitute $x = 8$ into the expression for $\angle GEF$: $m\angle GEF=4x + 13=4\times8+13=32 + 13=45^{\circ}$.

Answer:

$m\angle DEG = 135^{\circ}$, $m\angle GEF = 45^{\circ}$