# geometry

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
y=15
Now you can determine the measures.

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oobleck
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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