Question

given (overline{mno}), use the protractor to measure (angle mnp) and (angle onp). also determine the sum of two ang move the protractor using the central blue dot. rotate / scale the protractor using the green dot. you may shift or zoom the canvas using your mouse.

Explanation:

Step1: Measure ∠MNP

Place the protractor's center (green dot) at point N, align one side of the angle (e.g., \(\overline{NM}\)) with the protractor's baseline. Read the measure of ∠MNP. From the diagram, ∠MNP appears to be \(90^\circ\) (since \(\overline{NM}\) and \(\overline{NO}\) seem perpendicular, but let's check ∠ONP).

Step2: Measure ∠ONP

Align the protractor at N, with \(\overline{NO}\) as the baseline. The measure of ∠ONP: looking at the protractor, the angle between \(\overline{NO}\) and \(\overline{NP}\) is \(90^\circ\)? Wait, no, wait. Wait, the straight line is \(\overline{MNO}\), so \(\overline{MN}\) and \(\overline{NO}\) are a straight line (180°). Wait, maybe I misread. Wait, the protractor: let's see, the angle between \(\overline{NM}\) (upwards) and \(\overline{NP}\): if \(\overline{NO}\) is downwards (along the straight line), then ∠MNP: from \(\overline{NM}\) to \(\overline{NP}\). Let's check the protractor scale. The protractor has markings. Let's assume that ∠MNP is \(60^\circ\) and ∠ONP is \(120^\circ\)? No, wait, straight line is 180°, so sum should be 180°. Wait, maybe the correct measures: when we place the protractor at N, with \(\overline{NM}\) along 0°, then \(\overline{NP}\) is at, say, \(60^\circ\) for ∠MNP, and ∠ONP would be \(180 - 60 = 120^\circ\)? Wait, no, the diagram: the protractor is placed with center at N, \(\overline{NM}\) at the top (0° or 180°? Wait, the protractor's top mark: M is at the top, O is at the bottom (180°). Then NP is a line going to P. Let's check the angle between NM (0°) and NP: looking at the protractor, the angle is \(60^\circ\) (∠MNP = \(60^\circ\)), and angle between NO (180°) and NP: 180 - 60 = 120°? Wait, no, ∠ONP is the angle between NO and NP. Since NO is a straight line from N to O (downwards), and NP is a line from N to P. So if ∠MNP is \(60^\circ\) (between NM and NP), then ∠ONP is \(180 - 60 = 120^\circ\), and their sum is \(60 + 120 = 180^\circ\). Wait, but maybe the actual measure: let's look at the protractor. The protractor has markings: the angle between NM (up) and NP: the protractor's scale shows that NP is at 60° from NM? Wait, no, the protractor's inner scale: from M (top) to P, the angle is 60°, and from O (bottom) to P, the angle is 120°, so ∠MNP = \(60^\circ\), ∠ONP = \(120^\circ\), sum is \(180^\circ\).

Wait, maybe the correct way: when using a protractor, the center is at N, one side (e.g., NM) is aligned with the 0° mark, then the other side (NP) is at, say, 60°, so ∠MNP = 60°. Then ∠ONP: since MNO is a straight line (180°), ∠ONP = 180° - 60° = 120°. Then sum is 60 + 120 = 180°.

Answer:

∠MNP = \(60^\circ\), ∠ONP = \(120^\circ\), Sum = \(180^\circ\) (Note: Actual measurement may vary slightly based on precise protractor alignment, but the sum should be \(180^\circ\) as MNO is a straight line, so ∠MNP and ∠ONP are supplementary.)