In figure,   AB, CD and PQ are three lines concurrent at O. If ∠ AOP = 5y, ∠ QOD = 2y and ∠ BOC = 5y, find the value of y.
        

Lines AB, CD and PQ intersect at O.
∠ DOQ = 2y°, ∠ AOP = 5y° and ∠ COB = 5y°.
AB and CD intersect at O.
∠ COB = ∠ AOD (Vertically opposite angles)
∴ ∠ AOD = 5y (Since ∠ COB = 5y)
∠ AOP + ∠ AOQ = 180°
⇒ ∠ AOP + ∠ AOD + ∠ DOQ = 180°
⇒ 5y + 5y +  2y = 180°
⇒ 12y = 180°
⇒ y = = 15°
∴ The value of y = 15°.