Question

ABCD is a quadrilateral in which angle ABC is 73 degree and angle C is 97 degree and angle D is 110 degree if AE is parallel to DC abd BE parallel to AD and AE is intersects BC at F,find mesaure of ∠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°

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