In the adjoining figure, there coplanar lines AB, CD and EF intersect at a point O, forming angles as shown. Find the values of x, y, z and t.

X=4, Y=4, Z=50, t=90

Given, coplanar lines AB, CD and EF intersect at a point O.

Therefore, ∠AOF = ∠BOE ________________________ (i)

∠BOD = ∠AOC ________________________ (ii)

∠DOF = ∠COE ________________________ (iii)

x = y from equation (i)

t = 90 from equation (ii)

z = 50 from equation (iii)

∠AOF + ∠DOF + ∠BOD = 180° (from AOB straight line)

⇒ x + 50° + 90° = 180°

⇒ x = 180° - 140°

⇒ x = 40°

x = y = 40° from equation (i)