Question

#14: m∠efd = ____°
(11x - 3)° (6x + 13)°
#15: m∠nst = ____°
(2x - 9)° (3x - 1)°

Explanation:

Step1: Set up equation for #14

Since $\angle EFD$ and $\angle DFG$ are supplementary (linear - pair of angles, sum to 180°), we have $(11x - 3)+(6x + 13)=180$.
Combining like - terms: $11x+6x-3 + 13=180$, which simplifies to $17x+10 = 180$.
Subtract 10 from both sides: $17x=180 - 10=170$.
Divide both sides by 17: $x = 10$.
Then $m\angle EFD=11x - 3=11\times10-3=107$.

Step2: Set up equation for #15

Assume the right - angle at $S$ is 90°. The sum of the angles $\angle RSL+\angle LSN+\angle NST = 90°$. So $(2x - 9)+(3x - 1)=90$.
Combining like - terms: $2x+3x-9 - 1=90$, which simplifies to $5x-10 = 90$.
Add 10 to both sides: $5x=90 + 10 = 100$.
Divide both sides by 5: $x = 20$.
Then $m\angle NST=3x - 1=3\times20-1=59$.

Answer:

#14: 107
#15: 59