Ray BD is the bisector of ∠ABC. m∠ABD=2y-3, M∠DBC=y+12. Find the measure of ∠ABC.

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  1. If BD bisects the angle, then the two smaller angles are congruent.
    That means their measures are equal.
    That means that
    2y-3 = y+12
    Now you can determine the measures.

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  2. Statements
    Ray BD bisects ∠ABC
    m∠ABD = m∠DBC
    m∠ABD + m∠DBC = m∠ABC
    m∠ABD + m∠ABD = m∠ABC
    2m∠ABD = m∠ABC
    m∠ABD = ½m∠ABC

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