Question

In the given figure, BA || CE, EF || BC and EF = CF. The measures of ∠DFC and ∠CBD respectively are

• A. 42°, 56°
• B. 26°, 48°
• C. 18°, 56°
• D. 8°, 76°

Answer 1

The correct option is D 8°, 76°


Since BA || CE and BF is a transversal.
∴∠CDB = ∠DBA (Alternate interior angles)
⇒ ∠CDB = 56° .….(i)
Similarly, BC || EF and BF is a transversal.
∴∠CBD = ∠EFD (Alternate interior angles)
⇒ ∠CBD = 76° …..(ii)
In ΔBDC,
∠CDB + ∠CBD + ∠BCD = 180° (Angle sum property)
⇒ 56° + 76° + ∠BCD = 180° [From (i) and (ii)]
⇒ ∠BCD = 180° – 132º
⇒ ∠BCD = 48° …..(iii)
Now, BC || EF and CE is a transversal.
∴ ∠FEC = ∠BCE (Alternate interior angles)
⇒ ∠FEC = 48° [From (iv)] …..(v)
Now, in ΔEFC,
∠EFC + ∠FCE + ∠FEC = 180° (Angle sum property)
⇒ ∠EFC = 180° – 48° – 48° (EF = FC ⇒ ∠FCE = ∠FEC)
⇒ ∠EFC = 84°
⇒ ∠EFD + ∠DFC = 84°
⇒ ∠DFC = 84° – 76° = 8° (∵ ∠EFD = 76°)
Thus, the measures of ∠DFC and ∠CBD are 8° and 76° respectively.
Hence, the correct answer is option (d).