Question

ear pairs and vertical angles
what is the value of x?
35
60
70
20
(diagram: lines ts and vw intersect at r, with angle (x + 40)° at r between t and s, and angle (3x)° at r between v and w)

Explanation:

Step1: Identify vertical angles

The angles \((x + 40)^\circ\) and \((3x)^\circ\) are vertical angles, so they are equal.
\[x + 40 = 3x\]

Step2: Solve for \(x\)

Subtract \(x\) from both sides:
\[40 = 2x\]
Divide both sides by 2:
\[x = \frac{40}{2} = 20\]
Wait, but let's check again. Wait, maybe they are supplementary? Wait, no, the diagram: if the lines are intersecting, vertical angles are equal. Wait, maybe I made a mistake. Wait, let's re - examine. Wait, maybe the angles are supplementary? Wait, no, the labels: T - R - S and V - R - W are two lines intersecting at R. So \((x + 40)^\circ\) and \((3x)^\circ\) are vertical angles? Wait, no, maybe adjacent angles forming a linear pair? Wait, no, vertical angles are opposite each other. Wait, maybe the correct relationship is that they are equal (vertical angles). But when we solve \(x + 40=3x\), we get \(x = 20\). But let's check the answer options. 20 is an option. Wait, but let's verify. If \(x = 20\), then \(x + 40=60\) and \(3x = 60\), so they are equal. So that works.

Answer:

20 (the option with 20)