Question

question 18 (5 points) listen find x in the given figure. a) 168° b) 72° c) 120° d) 60°

Explanation:

Step1: Identify Vertical Angles

The angle of \(120^\circ\) and the angle adjacent to \(48^\circ\) and \(x\) (forming a linear pair or related by vertical angles) – first, note that the angle supplementary to \(120^\circ\) (since they are adjacent on a straight line) is \(180^\circ - 120^\circ = 60^\circ\)? Wait, no, actually, let's look at the lines. The line with \(120^\circ\) and the other line – maybe alternate interior angles? Wait, actually, the angle opposite to the one with \(48^\circ\) and \(x\) – let's re-examine. Wait, the sum around a point? Wait, no, let's see: the angle between the vertical line and the line with \(48^\circ\) and \(x\) – actually, the key is that the angle adjacent to \(120^\circ\) (on the straight line) is \(60^\circ\)? Wait, no, maybe the angle that is equal to the angle opposite? Wait, no, let's do it step by step.

Wait, the angle marked \(120^\circ\) and the angle that is supplementary to it (since they are on a straight line) is \(180 - 120 = 60^\circ\)? No, that's not right. Wait, actually, the lines: the two lines (the one with \(120^\circ\) and the other) are parallel? Wait, no, the figure has intersecting lines. Wait, maybe the angle \(x\) is related to \(48^\circ\) and the angle that is equal to \(180 - 120 = 60^\circ\)? Wait, no, let's think again.

Wait, the sum of angles around a point? Wait, no, the vertical line and the other lines. Wait, the angle \(x\), \(48^\circ\), and the angle that is equal to \(180 - 120 = 60^\circ\)? Wait, no, maybe the angle adjacent to \(120^\circ\) is \(60^\circ\) (since \(120 + 60 = 180\)), and then \(x + 48 + 60 = 180\)? Wait, no, that would be \(x = 180 - 48 - 60 = 72\)? Wait, that gives \(72^\circ\), which is option B. Wait, let's check:

Step 1: Find the angle supplementary to \(120^\circ\). Since they are on a straight line, \(180^\circ - 120^\circ = 60^\circ\).

Step 2: Now, the angles \(48^\circ\), \(60^\circ\), and \(x\) are on a straight line (vertical line), so their sum is \(180^\circ\). So \(48^\circ + 60^\circ + x = 180^\circ\)? Wait, no, that would be three angles, but actually, the vertical line and the two other lines: the angle \(48^\circ\), the angle we found (\(60^\circ\)), and \(x\) – wait, no, maybe the vertical line is a straight line, so the sum of angles on one side of the vertical line is \(180^\circ\). So \(48^\circ + \text{(angle from the other line)} + x = 180^\circ\). Wait, the angle from the other line is \(60^\circ\) (supplementary to \(120^\circ\)), so \(48 + 60 + x = 180\)? No, that would be \(108 + x = 180\), so \(x = 72\). Yes, that makes sense. So:

Step1: Find supplementary angle to \(120^\circ\)

The angle adjacent to \(120^\circ\) on a straight line is \(180^\circ - 120^\circ = 60^\circ\).

Step2: Sum of angles on a straight line

The angles \(48^\circ\), \(60^\circ\), and \(x\) are on a straight line (vertical line), so their sum is \(180^\circ\). Thus, \(48^\circ + 60^\circ + x = 180^\circ\)? Wait, no, that's three angles, but actually, the vertical line and the two lines: the angle \(48^\circ\), the angle \(60^\circ\) (from the other line), and \(x\) – wait, maybe the vertical line is a straight line, so the sum of angles on one side is \(180^\circ\). So \(48^\circ + 60^\circ + x = 180^\circ\)? Wait, no, that would be \(x = 180 - 48 - 60 = 72^\circ\). Yes, that's correct.

Answer:

B) \(72^\circ\)