Multiple Choice Questions on In the figure given below AB is parallel to CD ang ABC 65 deg ang CDE 15 deg and AB AE nbs........... for Mathematics - All Exams Preparation

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Multiple Choice Questions

In the figure given below AB is parallel to CD ang ABC 65 deg ang CDE 15 deg and AB AE nbs...........

Quantitative Aptitude ( CCS) Geometry
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    In the figure given below, AB is parallel to CD. ∠ABC = 65°, ∠CDE = 15° and AB = AE. What is the value of ∠AEF?

    30°

    Incorrect Answer

    35°

    Correct Answer

    40°

    Incorrect Answer

    45°

    Incorrect Answer
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    Explanation:
    Given that,
    ∠ABC = 65° and ∠CDE = 15°
    Here, ∠ABC + ∠TCB = 180°
    (?   AB || CD)
    ∠TCB = 180° – ∠ABC
    ∴   ∠TCB = 180° – 65° = 115°
    ?   ∠TCB + ∠DCB = 180°
    (Linear pair)
    ∴   ∠DCB = 65°
    Now, in ΔCDE
    ∠CED = 180° – (∠ECD + ∠EDC)
    (?   ∠ECD = ∠BCD)
    = 180° – (– 65° + 15° ) = 100°
    ?   ∠DEC + ∠FEC = 180°
    ⇒   ∠FEC = 180° – 100° = 80°
    Given that, AB = AE.
    i.e. ΔABE an isosceles triangle.
    ∴   ∠ABE = ∠AEB = 65°
    ?   ∠AEB + ∠AEF + ∠FEC = 180°
    (straight line)
    ⇒   65° + x° + 80° = 180°
    ∴   x° = 180° – 145° = 35°.

    By: Amit Kumar
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