Question

1. solve for w:

1. find x and y:

Explanation:

Step1: Solve for \( w \)

Vertical angles are equal. So, \( 8w + 8=9w - 5 \).
Subtract \( 8w \) from both sides: \( 8w+8 - 8w=9w - 5-8w \), which gives \( 8 = w - 5 \).
Add 5 to both sides: \( 8 + 5=w - 5+5 \).

Step2: Solve for \( x \)

Vertical angles are equal. So, \( 2x + 5=3x - 33 \).
Subtract \( 2x \) from both sides: \( 2x + 5-2x=3x - 33-2x \), which gives \( 5=x - 33 \).
Add 33 to both sides: \( 5 + 33=x - 33+33 \), so \( x = 38 \).

Step3: Solve for \( y \)

Since \( 2x + 5 \) and \( 4y - 1 \) are vertical angles (or we can use the fact that \( 3x - 33 \) and \( 4y - 1 \) can also be related through angle - pair properties. Substitute \( x = 38 \) into \( 2x+5 \): \( 2\times38 + 5=76 + 5=81\).
Set \( 4y - 1=81 \).
Add 1 to both sides: \( 4y-1 + 1=81 + 1\), so \( 4y=82 \).
Divide both sides by 4: \( y=\frac{82}{4}=\frac{41}{2}=20.5 \).

Answer:

For \( w \): \( w = 13 \).
For \( x \): \( x = 38 \).
For \( y \): \( y = 20.5 \).