Question

6x + 7
6y - 7
7x - 13
x = 20
y = 67/3

Explanation:

Step1: Set equal vertical - angles

Vertical - angles are equal. So, we set \(6x + 7=7x - 13\).

Step2: Solve for \(x\)

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

Step3: Find \(y\)

Since the sum of angles around a point is \(360^{\circ}\) and vertical - angles are equal, we can assume the other pair of vertical - angles are also equal. Let's use the fact that the angles are supplementary in a linear pair. But we can also just note that if we consider the relationship between the angles, and assume the figure has some symmetry of equal - angle relationships. Since we know \(x = 20\), we can set \(6y-7=6x + 7\) (assuming the non - \(x\) related angle is equal to one of the \(x\) related angles). Substitute \(x = 20\) into the equation: \(6y-7=6\times20 + 7\). First, calculate the right - hand side: \(6\times20+7 = 120 + 7=127\). So, \(6y-7 = 127\). Add 7 to both sides: \(6y-7 + 7=127 + 7\), which gives \(6y=134\). Divide both sides by 6: \(y=\frac{134}{6}=\frac{67}{3}\).

Answer:

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