Question

1. find x if m∠nml = 11x + 8, m∠nmd = 9x - 4, and m∠dml = 24°.

Explanation:

Step1: Identify angle - relationship

Since $\angle NML=\angle NMD+\angle DML$, we can set up an equation.
$$11x + 8=(9x - 4)+24$$

Step2: Simplify the right - hand side of the equation

Combine like terms on the right - hand side: $(9x - 4)+24=9x+(-4 + 24)=9x + 20$. So the equation becomes $11x + 8=9x+20$.

Step3: Isolate the variable terms

Subtract $9x$ from both sides of the equation: $11x-9x + 8=9x-9x+20$, which simplifies to $2x+8 = 20$.

Step4: Isolate the variable

Subtract 8 from both sides: $2x+8 - 8=20 - 8$, getting $2x=12$.

Step5: Solve for x

Divide both sides by 2: $\frac{2x}{2}=\frac{12}{2}$, so $x = 6$.

Answer:

$x = 6$