Question 1208365: Given: Triangle ABC, Bisectors of < a and < b meet at O. Prove: m (< aob) > 90 degrees
Answer by greenestamps(13209)   (Show Source):
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In triangle ABC, the sum of the three angle measures is 180 degrees, so the sum of the measures of angles A and B is less than 180.
In triangle AOB, angle OAB is half of angle A and angle OBA is half of angle B; therefore, the sum of the measures of angles OAB and OBA is less than 90 degrees.
Angle AOB is the third angle in triangle AOB; since the sum of the measures in that triangle is 180 degrees, the measure of angle AOB is greater than 90 degrees.
PROVED
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