Question

In the given figure, AB||CD. Find the value of x.

Answer 1

AB∥CD and AC is the transversal.
Then,
∠BAC+∠ACD=180° (Consecutive Interior Angles)

⇒75+∠ACD=180⇒∠ACD=105°
And,
∠ACD=∠ECF (Vertically-Opposite Angles)

⇒∠ECF=105°
We know that the sum of the angles of a triangle is 180°.
∠ECF+∠CFE+∠CEF=180°

⇒105°+30°+x=180°

⇒135°+x=180°

⇒x=45°