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Question

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


Solution

We know that if two lines intersect, then the vertically opposite angles are equal.

∴∠BOD = ∠AOC = 90°

Hence, t = 90°

Also,

∠DOF = ∠COE = 50°

Hence, z = 50°

Since AOB is a straight line, we have:

∠AOC + ∠COE + ∠BOE = 180°

⇒ 90 + 50 + y = 180°

⇒ 140 + y = 180°

⇒ y = 40°

Also,

∠BOE = ∠AOF = 40°

Hence, x = 40°

∴ x = 40°, y = 40°, z = 50° and t = 90°

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