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? asked in Science & MathematicsMathematics · 2 months ago

If ABCD is a kite how can I find angle C, when consecutive sides are congruent? (DA=AB, DC=CB)?

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1 Answer

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  • Ash
    Lv 7
    2 months ago
    Favorite Answer

    Join DB

    ADB forms isosceles triangle with AD ≅ AB 

    m∠ADB = m∠ABD ... (1)

    In Δ ADB,

    m∠ADB + m∠ABD + m∠A = 180°

    from (1)

     m∠ADB + m∠ADB  +  120° = 180°

    2m∠ADB  = 60°

    m∠ADB = 30°

    m∠ADC =  m∠ADB +  m∠BDC

    85° = 30° + m∠BDC

    m∠BDC = 55°

    Since DC ≅ BC

    m∠DBC = 55°

    In Δ DBC,

    m∠BDC + m∠DBC + m∠C = 180°

    55° +  55° + m∠C = 180°

    m∠C = 70°

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