In Fig. 6.35, Δ ODC ~ Δ OBA, ∠ BOC = 125° and ∠ CDO = 70°. Find ∠ DOC, ∠ DCO and ∠ OAB

 From the figure,

DOB is a straight line

∠ DOC + ∠ COB = 180°

∠ DOC = 180° - 125°

          = 55°

In ΔDOC,

∠ DCO + ∠ CDO + ∠ DOC = 180°

(Sum of the measures of the angles of a triangle is 180º)

∠ DCO + 70º + 55º = 180°

∠ DCO = 55°

It is given that ΔODC  ΔOBA

∠ OAB = ∠ OCD (Corresponding angles are equal in similar triangles)

∠ OAB = 55°