In the proof that vertically opposite angles are equal

MATHEMATICS · Single correct · CBSE · Mathematics · Introduction to Euclid's Geometry · Introduction to Euclid's Geometry

Problem

In the proof that vertically opposite angles are equal, two equations are written: ∠AOC+∠AOD=180∘\angle AOC + \angle AOD = 180^{\circ} and ∠AOD+∠DOB=180∘\angle AOD + \angle DOB = 180^{\circ}. Which logical principle allows the deduction ∠AOC=∠DOB\angle AOC = \angle DOB? (a) Common Notion: "If equals are added to equals, the wholes are equal" (b) Linear Pair Axiom (c) Common Notion: "If equals are subtracted from equals, the remainders are equal" (d) Supplementary Angles Theorem

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