Question

In the given figure, AB || CD || EF. If ∠ABC = 85°, ∠BCE = x° and ∠CEF = 130°, then x = ?
(a) 30
(b) 25
(c) 35
(d) 15

Answer 1

(c) 35

$EF\parallel CD\text{and}CE$ is the transversal.
$$\begin{gathered} \therefore \angle CEF+\angle ECD=180°\left[\text{Consecutive Interior Angles}\right] \\ \Rightarrow 130°+\angle ECD=180° \\ \Rightarrow \angle ECD=50° \end{gathered}$$
Also, $AB\parallel CD\text{and}BC$ is the transversal.
$$\begin{gathered} \therefore \angle ABC=\angle BCD\left[\text{Alternate Interior Angles}\right] \\ \Rightarrow 85°=\angle BCE+\angle ECD \\ \Rightarrow 85°=x+50° \\ \Rightarrow x=35° \end{gathered}$$