Question

a table makes the angle shown with the floor. what must be the value of x in order for the top of the table to be parallel with the ground? a 30° b 45° c 55° d 90° e 135°

Explanation:

Step1: Recall parallel - line property

When two lines are parallel, corresponding angles are equal. The angle formed by the table - leg with the ground and the angle formed by the table - leg with the table top are corresponding angles if the table top is parallel to the ground.

Step2: Use angle - relationship

The angle given with the ground is \(135^{\circ}\). The angle \(x\) and the given \(135^{\circ}\) angle are corresponding angles. For the top of the table to be parallel to the ground, \(x\) must be equal to the angle formed by the table - leg and the ground. Since the sum of an angle and its supplementary angle is \(180^{\circ}\), and the non - parallel angle related to the \(135^{\circ}\) angle and \(x\) is supplementary to \(135^{\circ}\), we know that \(x = 135^{\circ}\) because of the corresponding - angles postulate for parallel lines.

Answer:

E. \(135^{\circ}\)