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Question

In the given figure, AB || CD. If ∠OAB = 124° and ∠OCD = 136°, then ∠AOC = ?
(a) 80°
(b) 90°
(c) 100°
(d) 110°

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Solution

(c) 100°

Draw OLABCD.
Now, OLAB and OA is the transversal.
AOL+OAB=180° Angles on the same side of a transversal line are supplementaryAOL+124°=180°AOL=56°
Also,
OLCD and OC is the transversal.
DCO+COL=180° Angles on the same side of a transversal line are supplementary136°+COL=180°COL=44°
Therefore,
AOC=AOL+COLAOC=56+44°AOC=100°

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