In the adjoining, there coplanar lines AB, CD and EF intersect at a point O. Find the value of x. Hence, find,and .

X=18,=36°,=90°,=54°

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

Therefore, ∠AOD = ∠BOC ________________________ (i)

∠BOF = ∠AOE ________________________ (ii)

∠COE = ∠DOF ________________________ (iii)

∠BOC = 2x from equation (i)

∠AOE = 3x from equation (ii)

∠DOF = 5x from equation (iii)

∠AOD + ∠DOF + ∠BOF + ∠BOC + ∠COE + ∠AOE = 360°

⇒ 2x + 5x + 3x + 2x + 5x + 3x = 360°

⇒ 20x = 360°

⇒ x = 18°

∠AOD = 2x = 2× 18° = 36°

∠COE = 3x = 3× 18° = 54°

∠AOE = 4x = 4× 18° = 72°