Question

In the given figure, three coplanar lines AB, CD, and EF intersect at point O. Find the values of x, y, z, and t.

• A. x = 40, y = 40, z = 90, t = 50
• B. x = 50, y = 40, z = 40, t = 90
• C. x = 40, y = 40, z = 50, t = 140
• D. x = 40, y = 40, z = 50, t = 90

Answer 1

The correct option is D x = 40, y = 40, z = 50, t = 90

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

∴ ∠BOD = ∠AOC = 90°
Hence, t = 90.

Similarly, ∠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°
Hence, y = 40.

Also, ∠BOE = ∠AOF = 40°
[Vertically opposite angles]
Hence, x = 40.

∴ x = 40, y = 40, z = 50, t = 90