Question

what is the measure of this angle? m\angle abc = ?^\circ

Explanation:

Step1: Identify the scale reading

Read the scale where the terminal sides of the angle lie. The inner - scale (assuming the correct scale for the angle's measurement) gives the values. The initial side (closer to \(0/360\)) is at \(10^{\circ}\) (if we consider the correct orientation of the protractor for the angle \(\angle ABC\)) and the terminal side is at \(290^{\circ}\). But wait, no, actually, when measuring an angle with a protractor, we use the difference between the two scale readings. If we assume the angle is measured as the difference between \(290^{\circ}\) and \(10^{\circ}\) (subtracting the smaller non - reflex angle measure).

Step2: Calculate the angle measure

We use the formula \(m\angle ABC=\vert\theta_1 - \theta_2\vert\). Here, \(\theta_1 = 290^{\circ}\) and \(\theta_2=10^{\circ}\). So \(m\angle ABC=290 - 10\)

Answer:

\(280^{\circ}\)