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In triangle ΔABC, ∠C is a right angle and CD is the height to AB. Find the angles in ∠ACD and ∠BCD if:

m∠A = 65°

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  1. 5 May, 00:34
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    Given:

    m∠C = 90°, because ∠C is a right angle.

    m∠D = 90°, because CD is the height to AB.

    m∠A = α

    Because the sum of angles in a triangle is 180°, therefore

    m∠DBC + 90° + α = 180°

    m∠DBC = 90° - α

    Again, for the same reason,

    m∠DCB + m∠DBC + 90° = 180°

    m∠DCB + 90° - α + 90° = 180°

    m∠DCB = α

    For the same reason,

    m∠ACD + 90° + α = 180°

    m∠ACD = 90° - α

    m∠ADC = 90° (by definition)

    m∠CDB = 90° (by definition)

    Answer:

    m∠DBC = 90° - α

    m∠DCB = α

    m∠CDB = 90°

    m∠ACD = 90° - α

    m∠ADC = 90°

    Step-by-step explanation:

    Learned this several times, also had this problem in my notes; )
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