In the figure, two straight lines AB and CD intersect at O. If ∠COT = 60°, find a, b, c.

Since AB and CD intersect at O
⇒ ∠BOD = ∠AOC
     ⇒ a = 4b …. (i)
Also a + b + 60° = 180°
           Þ a + b = 120° …. (ii)
         or 4b + b = 120°
              ⇒ 5b = 120° 
                ⇒ b = 24°
⇒ a = 4b = 4 x 24 = 96°
Since ∠AOD = ∠COB …. (Vertically opposite angles)
         ⇒ 2c = 60° + b
         ⇒ 2c = 60° + 24° = 84°
          .^.. c = 42°
Hence a = 96°, b = 24°, c = 42°