Question

6x + 7
6y - 7
7x - 13
x = type your answer...
y = type your answer...

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. So, we set up the equation for \(x\): \(6x + 7=7x - 13\).

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides: \(6x+7 - 6x=7x - 13-6x\), which simplifies to \(7=x - 13\). Then add 13 to both sides: \(7 + 13=x-13 + 13\), so \(x = 20\).

Step3: Use the fact that adjacent angles are supplementary (assuming the lines are straight and the angles form a linear - pair) or another angle - relationship (if applicable). Since vertical angles are equal, we can set up an equation for \(y\). Let's assume the non - given relationship for simplicity, if we consider the equality of vertical angles, we can set \(6y-7 = 6x + 7\). Substitute \(x = 20\) into the equation: \(6y-7=6\times20 + 7\).

Step4: Solve the equation for \(y\)

First, simplify the right - hand side: \(6y-7=120 + 7=127\). Then add 7 to both sides: \(6y-7 + 7=127+7\), which gives \(6y=134\). Divide both sides by 6: \(y=\frac{134}{6}=\frac{67}{3}\approx22.33\).

Answer:

\(x = 20\)
\(y=\frac{67}{3}\)