In figure,   three lines p, q and r are concurrent at O. If a = 50° and b = 90°, find c, d, e and f.
       

Given: Three coplanar lines AB, CD and PQ meet at O.
      ∠ BOQ = a = 50° and ∠ BOC = b = 90°
To find: c, d, e and f.
Proof: Adjacent angles, ∠ BOQ, ∠ BOP form a linear pair.
    .^.. ∠ BOQ + ∠ BOP = 180° (Linear Pair Axiom)
a + ∠ BOC + ∠ COP = 180°
                  a + b + c = 180°
               50° + 90° + c = 180° (given)
                                  c = 180°- (90° + 50°)
                                     = 180° - 140°
                                     = 40°
 d = a = 50° (Vertically opp. angles)
 e = b = 90° (Vertically opp. angles)
 f = c = 40° (Vertically opp. angles).