Question

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

Explanation:

Step1: Use corresponding - angles property

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

$$\begin{align*} 2x+18&=4x - 14\\ 18 + 14&=4x-2x\\ 32&=2x\\ x& = 16 \end{align*}$$

\]

Step2: Find the value of \((4x - 14)^{\circ}\)

Substitute \(x = 16\) into \((4x - 14)^{\circ}\), we get \(4\times16-14=64 - 14=50^{\circ}\).

Step3: Use linear - pair property

The angle \((4x - 14)^{\circ}\) and \(y^{\circ}\) form a linear - pair. So \((4x - 14)+y = 180\). Since \(4x - 14 = 50\), then \(y=180-(4x - 14)=180 - 50=130^{\circ}\).

Answer:

130