Question

use the diagram to complete the statements. the angle of depression from point r to point s is angle 3. the angle of elevation from point s to point r is angle 4. angle 2 is the angle of elevation from point q to point r. angle 1 is the angle of dropdown options: elevation from point q to point r, elevation from point r to point q, depression from point q to point r, depression from point r to point q. diagram: points q, r, s with dashed horizontal lines and angles labeled 1, 2, 3, 4.

Explanation:

Step1: Recall angle of depression/elevation

Angle of depression: from higher to lower, horizontal line down to line of sight.
Angle of elevation: from lower to higher, horizontal line up to line of sight.

Step2: Analyze Angle 1

Point Q is higher than R. The horizontal line at Q (dashed) and line QR form Angle 1. From Q to R, if we consider R's position, but Angle 1 is at Q? Wait, no: the horizontal at R is the middle dashed line. Wait, Q's dashed line is horizontal (top), R's is middle, S's is bottom.

Angle 1: at Q, between horizontal (top dashed) and QR. But angle of depression from Q to R? No, angle of depression from R to Q? Wait, no: angle of depression is when looking down from a higher point. Wait, R is between Q (top) and S (bottom). Wait, the horizontal lines: Q's dashed is horizontal (same level as Q), R's dashed is horizontal (middle), S's dashed is horizontal (same level as S).

So, angle of depression from Q to R: no, Q is higher than R? Wait, Q is left, R is middle, S is left-bottom? Wait, the diagram: Q is top-left, R is middle-right, S is bottom-left. The dashed lines: Q's dashed is horizontal (rightward), R's dashed is horizontal (leftward), S's dashed is horizontal (rightward).

So, line QR: from Q (top-left) to R (middle-right). The horizontal at Q is rightward dashed. Angle 1 is between Q's horizontal and QR.

Angle of depression from Q to R? No, angle of depression is when the observer is at a higher point, looking down to a lower point. Wait, R is below Q? No, R is to the right of Q. Wait, maybe the horizontal lines are all parallel (since they are dashed and horizontal). So, the horizontal line at Q (dashed right), horizontal at R (dashed left), horizontal at S (dashed right).

So, angle of depression from Q to R: no, angle of depression is the angle between horizontal (at observer) and line of sight down to the object. If observer is at Q, looking down to R? But R is to the right, not down. Wait, maybe the vertical? No, the problem is about horizontal lines.

Wait, the options: "depression from point Q to point R" – no, depression is down. Wait, "depression from point R to point Q": observer at R, looking up to Q? No, depression is down. Wait, angle of depression from Q to R: observer at Q, horizontal line (right) and line QR (downward to R? No, QR is going to the right and down? Wait, Q is top-left, R is middle-right, so QR is a line going down and right. So the horizontal at Q is right (horizontal), and QR is down-right. So angle 1 is the angle between Q's horizontal (right) and QR (down-right) – that's angle of depression from Q to R? No, angle of depression is when the observer is at Q, looking down to R (which is below Q's horizontal level). Wait, maybe the horizontal lines are all at the same vertical level? No, Q is top, S is bottom, R is middle. So Q is higher than S, R is between Q and S vertically?

Wait, the key: angle of depression is equal to angle of elevation (alternate interior angles, since horizontal lines are parallel).

So, angle of depression from Q to R: observer at Q, horizontal line (right) and line QR (down to R) – angle of depression. But the options: "depression from point Q to point R" – no, the option is "depression from point Q to point R" or "depression from point R to point Q". Wait, the correct option: angle 1 is the angle of depression from point Q to point R? No, the options include "depression from point Q to point R" – no, the options are:

- elevation from point Q to point R
- elevation from point R to point Q
- depression from point Q to point R
- depression from point R to point Q

Wait, angle of depression from R to Q: observer at R, looking up to Q? No, depression is down. Wait, angle of elevation from R to Q: observer at R, looking up to Q (since Q is above R? Wait, Q is to the left, R is to the right. Maybe vertically, Q is above R? The diagram: Q is top, R is middle, S is bottom. So Q is above R, R is above S. So horizontal lines: Q's horizontal (same level as Q), R's horizontal (same level as R), S's horizontal (same level as S). So Q is above R, R is above S.

So, line QR: from Q (above) to R (middle). The horizontal at Q is horizontal (same level as Q), so angle of depression from Q to R is the angle between Q's horizontal and QR (down to R). But angle 1 is at Q, between Q's horizontal and QR. So angle of depression from Q to R? But the options have "depression from point Q to point R" – no, the option is "depression from point Q to point R" – but that would be angle of depression from Q to R. Wait, no, angle of depression is when the observer is at Q, looking down to R (which is below Q's level). So yes, angle 1 is the angle of depression from Q to R? No, the options: "depression from point Q to point R" – but the correct answer is "depression from point Q to point R"? Wait, no, the options:

Wait the dropdown options:

- elevation from point Q to point R
- elevation from point R to point Q
- depression from point Q to point R
- depression from point R to point Q

Wait, angle of depression from Q to R: observer at Q, horizontal line (same level as Q) and line of sight to R (below Q's level) – angle of depression. But angle 1 is at Q, between Q's horizontal (right) and QR (down-right). So that's angle of depression from Q to R? But the correct answer is "depression from point Q to point R"? Wait, no, maybe I got it wrong. Wait, angle of depression is the angle between the horizontal (at observer) and the line of sight when the object is below the observer. So if Q is above R (vertically), then R is below Q, so observer at Q, looking down to R: angle of depression. So angle 1 is that angle. But the options: "depression from point Q to point R" – yes. Wait, but the other options: "depression from point R to point Q" – observer at R, looking down to Q? But Q is above R, so that would be angle of elevation, not depression.

Wait, no, angle of elevation is from lower to higher: observer at lower point, looking up to higher point. Angle of depression is from higher to lower: observer at higher point, looking down to lower point.

So, angle 1: at Q (higher point), between horizontal (at Q) and line QR (down to R, lower point? Wait, R is to the right, not down. Maybe the vertical axis: Q is higher (top), R is middle (vertically), S is bottom. So Q is above R, R is above S. So horizontally, Q is left, R is right, S is left-bottom. So line QR: from Q (left-top) to R (right-middle) – so it's a line going down and right. The horizontal at Q is right (horizontal), so angle 1 is between Q's horizontal (right) and QR (down-right) – that's angle of depression from Q to R. But the options: "depression from point Q to point R" – yes. Wait, but the correct answer is "depression from point Q to point R"? Wait, no, the options: "depression from point Q to point R" – but let's check the other options.

Wait, "elevation from point R to point Q": observer at R (middle), looking up to Q (top) – that's angle of elevation. But angle 1 is at Q, not at R. So angle 1 is at Q, so the observer is at Q. So angle of depression from Q to R: observer at Q, horizontal line (right) and line of sight to R (down-right) – angle of depression. So the correct option is "depression from point Q to point R"? Wait, no, the options: "depression from point Q to point R" – yes. Wait, but let's re-examine the diagram.

Wait, the horizontal lines: Q's dashed is horizontal (same level as Q), R's dashed is horizontal (same level as R), S's dashed is horizontal (same level as S). So Q is above R, R is above S. So the line QR: from Q (above) to R (middle) – the angle between Q's horizontal (right) and QR is angle 1. So that's angle of depression from Q to R. So the correct option is "depression from point Q to point R". Wait, but the options include "depression from point Q to point R" – yes. So that's the answer.

Answer:

depression from point Q to point R