Question

In the given figure, OB is perpendicular to OA and ∠BOC = 49°. Find ∠AOD.

Answer 1

Given that ∠AOB = 90°  ......[∵ OB ⊥ OA]

⇒ ∠BOC + ∠COA = 90°

⇒ ∠COA = 90° – 49°  ......[∵ ∠BOC = 49° (given)]

⇒ ∠COA – 41°   ......(i)

Now, CD is a straight line.

∴ ∠AOD + ∠AOC = 180°  ......[Linear pair]

⇒ ∠AOD = 180° – 41°  ......[Using (1)]

∴ ∠AOD = 139°