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Point M is in the interior of angle AOB, the ray OC is a bisector of this angle. Prove that the measure of angle MOC is equal to one-half the difference of the measure of angles AOM and BOM

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olayemiolakunle65

Answer:

Step-by-step explanation:

Given: point M,

           m<AOB,

           OC the bisector of m<AOB

Thus,

m<AOC = m<BOC (bisector property of OC)

m<MOC = m<BOM (congruence property)

m<AOM - m<BOM = m<AOC = m<BOC

m<BOC = m<MOC = [tex]\frac{m<AOC}{2}[/tex]  (angle property)

Therefore,

m<AOM > m<BOM (point M location property)

m<MOC = [tex]\frac{m<AOM - m<BOM}{2}[/tex]

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