Question

if (mangle tuv=(9x + 1)^{circ}), (mangle tuw=(7x - 9)^{circ}), and (mangle wuv=(5x - 11)^{circ}), find the value of (x).

Explanation:

Step1: Use angle - addition postulate

Since $\angle TUV=\angle TUW+\angle WUV$, we can set up the equation $(9x + 1)=(7x - 9)+(5x - 11)$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $(7x - 9)+(5x - 11)=7x+5x-9 - 11=12x-20$. So the equation becomes $9x + 1=12x-20$.

Step3: Isolate the variable terms

Subtract $9x$ from both sides: $9x + 1-9x=12x-20-9x$, which simplifies to $1 = 3x-20$.

Step4: Solve for $x$

Add 20 to both sides: $1+20=3x-20 + 20$, so $21 = 3x$. Then divide both sides by 3: $\frac{21}{3}=\frac{3x}{3}$, and $x = 7$.

Answer:

7