Question

In the following figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB.

Answer 1

DOB is a straight line.

∴ ∠DOC + ∠COB = 180°

⇒ ∠DOC = 180° − 125°

⇒ ∠DOC = 55°

In ΔDOC,

∠DCO + ∠CDO + ∠DOC = 180°

(Sum of the measures of the angles of a triangle is 180°.)

⇒ ∠DCO + 70° + 55° = 180°

⇒ ∠DCO = 55°

It is given that ΔODC ∼ ΔOBA

∴ ∠OAB = ∠OCD           ...[Corresponding angles are equal in similar triangles.]

⇒ ∠OAB = 55°