Question

parallel lines e and f are cut by transversal b. what is the value of y? (2x + 18)° (4x - 14)° y° 16 50 130 164

Explanation:

Step1: Use corresponding - angles property

Since parallel lines \(e\) and \(f\) are cut by transversal \(b\), the corresponding angles \((2x + 18)^{\circ}\) and \((4x-14)^{\circ}\) are equal. So, \(2x + 18=4x - 14\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(18 = 2x-14\). Then add 14 to both sides: \(18 + 14=2x\), which gives \(32 = 2x\). Divide both sides by 2, so \(x = 16\).

Step3: Find the value of one of the angles

Substitute \(x = 16\) into \(2x + 18\): \(2\times16+18=32 + 18=50^{\circ}\).

Step4: Use the linear - pair property

The angle \((2x + 18)^{\circ}\) and \(y^{\circ}\) form a linear - pair. Since the sum of angles in a linear - pair is \(180^{\circ}\), and \((2x + 18)=50^{\circ}\), then \(y=180 - 50=130^{\circ}\).

Answer:

C. 130