Question

if a // b and e // f, what is the value of y? o 87 o 88 o 91 o 92

Explanation:

Step1: Use property of parallel lines

Since \(a\parallel b\) and \(e\parallel f\), the angles \((x + 1)^{\circ}\) and \((x - 3)^{\circ}\) are same - side interior angles. The sum of same - side interior angles of two parallel lines is \(180^{\circ}\). So, \((x + 1)+(x - 3)=180\).

Step2: Solve the equation for \(x\)

Simplify the left - hand side of the equation: \(x + 1+x - 3=180\), which gives \(2x-2 = 180\). Add 2 to both sides: \(2x=180 + 2=182\). Divide both sides by 2: \(x=\frac{182}{2}=91\).

Step3: Find the value of \(y\)

The angle \(y^{\circ}\) and \((x + 1)^{\circ}\) are corresponding angles. Since \(x = 91\), then \(x+1=91 + 1=92\). And because corresponding angles of parallel lines are equal, \(y = 92\).

Answer:

92