Question

In the given figure, AB || CD. If $\angle CAB={80}^o$ and $\angle EFC={25}^o$, then ∠CEF = ____.

• A. ${65}^{\circ }$
• B. ${75}^{\circ }$
• C. ${55}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is C ${55}^{\circ }$

Let $\angle CEF=x^o$
Now, AB || CD and AF is a transversal.
Therefore, $\angle DCF=\angle CAB={80}^o$ [Corresponding angles]
In ΔCEF, side EC has been produced to point D.
⇒ $x^o+{25}^o={80}^o$ [Sum of two opposite interior angles = exterior angle]
⇒ $x^o={80}^o-{25}^o$
⇒ $x^o={55}^o$