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ABCD is a quadrilateral in which …

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ABCD is a quadrilateral in which angleABC= 73° angleC= 97° and angleD=110°. If AE||DC,BE||AD and AE intersect BD at F, find angle BEF

    • Posted by Bhavay Goel 3 years, 8 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Khushi Kaur 3 years, 8 months ago

    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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