In ∆BOA, bisectors BK and OP are drawn, intersecting at point M, and the angle ОМB is equal to 100 °. Find the BAO angle.
The angles of a triangle add up to 180 degrees.
Consider ∆OMB, in which the sum of the angles BOM and MBO = 80 degrees (180 – OMB). Since OP and BK are bisectors, the sum of the angles BOA and OBA = 160 degrees. Then the angle BAO = 180 – (BOA + OBA) = 180 – 160 = 20 (degrees).
Answer: BAO angle = 20 degrees.
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