Question

question 4 (1 point) using the following diagram, find the value of x and y. if necessary, state your solution as an improper fraction. (25x + 8)° (9x + 2)° (7y + 5)° blank 1: x = blank 2: y =

Explanation:

Step1: Set up equation for vertical - angles

Vertical angles are equal. So, \(25x + 8=9x + 2\).
\[25x+8 = 9x + 2\]

Step2: Solve for \(x\)

Subtract \(9x\) from both sides: \(25x-9x+8=9x - 9x+2\), which simplifies to \(16x+8 = 2\). Then subtract 8 from both sides: \(16x+8 - 8=2 - 8\), getting \(16x=-6\). Divide both sides by 16: \(x=\frac{-6}{16}=-\frac{3}{8}\).
\[x =-\frac{3}{8}\]

Step3: Set up another equation

We assume the other pair of vertical - angles gives us an equation to solve for \(y\). Let's assume the other pair of vertical angles gives \(7y + 5=9x + 2\) (since we have used one pair of vertical - angles to find \(x\)). Substitute \(x =-\frac{3}{8}\) into the equation:
\[7y+5=9\times(-\frac{3}{8})+2\]
\[7y+5=-\frac{27}{8}+2\]
\[7y+5=-\frac{27}{8}+\frac{16}{8}\]
\[7y+5=-\frac{11}{8}\]
Subtract 5 from both sides: \(7y=-\frac{11}{8}-5=-\frac{11}{8}-\frac{40}{8}=-\frac{51}{8}\). Then divide both sides by 7: \(y =-\frac{51}{56}\).
\[y=-\frac{51}{56}\]

Answer:

Blank 1: \(x =-\frac{3}{8}\)
Blank 2: \(y =-\frac{51}{56}\)