Question

ABCD is a quadrilateral in which angle ABC is 73 degree and abgle C is 97 degree and angle D is 110degree if AE is parallel to DC abd BE parallel to AD and AE is intersects BC at F . Find angle EBF

Answer 1

Solution:-
Given AE is parallel to DC and BE is parallel to AD, ∠ ABC = 73°, C = 97°
To find : ∠ EBF
Since AE is parallel to DC
∴ 110° + ∠ DAE = 180°
(Co-interior ∠'s)
Also, ∠ BEA = ∠ DCF = 97° (Corresponding B ∠'s)
⇒ ∠ BEA = 97°
Now in Δ ABF,
∠ FAB + ∠ ABF + ∠ AFB = 180°  (Angle Sum Property)
⇒ ∠ FAB + 73° + 97° = 180°
⇒ ∠ FAB = 180°-170°
⇒ ∠ FAB = 10°
Now, AD is parallel to BE (Given)
∴ ∠ DAB + ∠ ABE = 180°  ( Co-interior angles)
⇒ ∠ DAF + ∠ FAB + ∠ ABF + ∠ EBF = 180°
⇒ 70° + 10° + 73° + ∠ EBF = 180°
∠ EBF = 180°- 153°
∠ EBF = 27°

Answer 2

see diagram.

Draw CG parallel to DA.  So DC is a traversal between parallel lines.
angle DCG = 180° -  ∠D = 180° - 110 °= 70°angle GCB = 97° - 70° = 27°angle EBF = angle GCB = 27°