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It is given that angle AOC = angle BOD (two angles around point O), and these share a common middle angle angle COD which lies inside both. Subtracting the common angle COD from each, what can be concluded?
(angle AOC = angle AOD + angle DOC and angle BOD = angle BOC + angle COD pattern: here treat angle AOC and angle BOD as wholes each containing angle COD.)

Class 9Euclid's AxiomsGeometry — Foundations
  • Aangle AOD = angle BOC, by subtracting equals from equals
  • Bangle AOD > angle BOC, by whole greater than part
  • Cangle AOD = angle BOD, by coincidence
  • Dangle AOD = angle COD, by addition of equals

Step-by-Step Solution

angle AOC = angle BOD (equals). Removing the common angle COD from each whole leaves equal remainders: angle AOD = angle BOC (equals subtracted from equals leave equal remainders).
Answer: A) angle AOD = angle BOC, by subtracting equals from equals

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