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geometry

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ABCD is a convex quadrilateral satisfying AB=BC=CD,AD=DB and ∠BAD=75∘. What is the measure of ∠BCD?

  • geometry -

    Since AD=DB, triangle ABD is isosceles, so
    ∠DAB = ∠DBA = 75° and ∠ADB = 30°

    Now draw AC, and again we have isosceles triangles ABC and BCD.

    ∠BCD = 75°

  • geometry -

    150

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