Question

1. find x if m∠uvy = 6x - 8, m∠uyw = 95°, and m∠ywv = 6x + 7. remember to show your work.
2. find x if m∠uvw = 90°, and m∠wvn = 9x - 1, m∠uvn = 31x + 1. remember to show your work.

Explanation:

Step1: Set up equation

Since $\angle{UVW}=\angle{UVY}+\angle{YWV}$, we have $95=(6x - 8)+(6x + 7)$.

Step2: Simplify the right - hand side

Combine like terms: $(6x - 8)+(6x + 7)=6x+6x-8 + 7=12x-1$. So the equation becomes $95 = 12x-1$.

Step3: Solve for x

Add 1 to both sides: $95 + 1=12x-1 + 1$, which gives $96 = 12x$. Then divide both sides by 12: $x=\frac{96}{12}=8$.

for question 20:

Step1: Set up equation

Since $\angle{UVN}=\angle{UVW}+\angle{WVN}$, we have $90=(31x + 1)+(9x-1)$.

Step2: Simplify the right - hand side

Combine like terms: $(31x + 1)+(9x-1)=31x+9x+1 - 1=40x$. So the equation becomes $90 = 40x$.

Step3: Solve for x

Divide both sides by 40: $x=\frac{90}{40}=\frac{9}{4}=2.25$.

Answer:

$x = 8$