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Question

In the given figure,OAB=75,OBA=55 and OCD=100. Then, ODC=?


(a)20

(b)25

(c)30

(d)35


Solution

(c) 30°

In ∆OAB, we have:

∠OAB+∠OBA+∠AOB=180° [ Sum of the angles of a triangle]

⇒75°+55°+∠AOB=180°

⇒∠AOB=50°

∴∠COD=∠AOB=50° Vertically-Opposite Angles

In ∆OCD, we have:

∠COD+∠OCD+∠ODC=180° [Sum of the angles of a triangle]

⇒50°+100°+∠ODC=180°

⇒∠ODC=30°

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