Question

the value of x is
84
96
132
264

Explanation:

Step1: Find the adjacent angle of 132°

The adjacent angle of \(132^{\circ}\) is \(180 - 132=48^{\circ}\) (supplementary angles).

Step2: Find the adjacent angle of 134°

The adjacent angle of \(134^{\circ}\) is \(180 - 134 = 46^{\circ}\) (supplementary angles).

Step3: Use the sum of angles in a triangle

In the triangle formed, we know that the sum of angles in a triangle is \(180^{\circ}\). Let the third angle in the triangle be \(y\). Then \(y=180-(48 + 46)=86^{\circ}\)

Step4: Use the property of parallel lines (consecutive - interior angles)

Since the lines are parallel, \(x + y=180^{\circ}\) (consecutive - interior angles). Substitute \(y = 84^{\circ}\), we get \(x=180 - 84=96^{\circ}\)

Answer:

96