Question

Mark (✓) against the correct answer.
In the given figure, CE || BA and EF || CD. If ∠BAC = 40°, ∠ACB = 65° and ∠CEF = x° then the value of x is
(a) 40
(b) 65
(c) 75
(d) 105
Figure

Answer 1

(d) 105

$$\begin{gathered} CE\parallel AB \\ \therefore \angle ACE=\angle BAC=40°\left(\mathrm{Alternate}\mathrm{angles}\right) \\ \therefore \angle BCE=\angle BCA\hspace{0.17em}+\angle ACE=65°+40°=105° \\ \mathrm{Again}EF\parallel CD\mathrm{and}\mathrm{line}\mathrm{segment}EC\mathrm{intersect}s\mathrm{them}. \\ \therefore \angle CEF=\angle BCE\left(\mathrm{alternate}\mathrm{angle}\right) \\ \Rightarrow x°=105° \\ \mathrm{Therefore},x=105. \end{gathered}$$