Question

In the given figure, if AB || CD, CD || EF and y : z = 3 : 7, x = ?
(a) 108°
(b) 126°
(c) 162°
(d) 63°

Answer 1

(b) 126°
Let $y=\left(3a\right)°\text{and}z=\left(7a\right)°$
Let the transversal intersect AB at P, CD at O and EF at Q.

Then, we have:
$$\begin{gathered} \angle COP=\angle DOF=y\left[\text{Vertically-Opposite Angles}\right] \\ \therefore \angle OQF+\angle DOQ=180°\left[\text{Consecutive Interior Angles}\right] \\ \Rightarrow 3a+7a=180° \\ \Rightarrow 10a=180° \\ \Rightarrow a=18° \\ \therefore y=3\times 18°=54° \end{gathered}$$
Also,
$$\begin{gathered} \angle APO+\angle COP=180° \\ \Rightarrow x+54°=180° \\ \Rightarrow x=126° \end{gathered}$$