Ravi draws two straight lines that intersect at point O. Lines AOB and COD are both straight lines. Going clockwise around O, the four angles are: angle AOC = (5m − 3)°, angle COB = (2m + 8)°, angle BOD, and angle DOA. Ravi draws ray OE that bisects angle BOD. What is angle EOA?
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Worked Solution
Step 1: Straight-line sum along AOB.
(5m − 3) + (2m + 8) = 180
7m + 5 = 180; m = 25
Step 2: angle AOC = 5(25) − 3 = 122°; angle COB = 2(25) + 8 = 58°
Step 3: Vertically opposite: angle BOD = 122°; angle DOA = 58°
Step 4: OE bisects angle BOD: angle BOE = angle EOD = 61°
Step 5: angle EOA = angle EOD + angle DOA = 61° + 58° = 119°
Correct answer: 119°
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