Question

Question was provided via image upload.

Explanation:

Step1: Analyze the angle relationship

The green arc represents a \(160^\circ\) angle from the negative x - axis to the positive y - axis (or vice - versa in terms of the arc). The angle we want to find is the acute angle between the blue line and the positive x - axis. We know that the angle between the negative x - axis and the positive x - axis is \(180^\circ\). So, to find the angle between the blue line and the positive x - axis, we can use the formula: \(\theta=180^\circ - 160^\circ\)

Step2: Calculate the angle

\(\theta = 180^\circ-160^\circ=20^\circ\)

Answer:

The measure of the angle (the acute angle between the blue line and the positive x - axis) is \(20^\circ\)