The four angles at a crossing: vertically opposite and linear pairs

What to assume they know

An angle as an amount of turning, measured in degrees, and reading a protractor
A straight line makes 180° at any point on it (the straight angle)
A letter-number stands for any number, not one number and the Class 6 work on angles: naming an angle by its vertex, and comparing angles as larger or smaller
Two numbers that add to a fixed total: if one goes up the other goes down
The habit of labelling parts of a figure with letters so they can be argued about

What they should be able to do

State how many angles two intersecting lines form, and how many different measures those angles can have
Given one of the four angles at a crossing, work out the other three by reasoning rather than by measuring
Identify every linear pair and every pair of vertically opposite angles in a labelled crossing
Explain why linear pairs add to 180°, from the straight angle
Reconstruct the argument that vertically opposite angles are equal, using letters rather than a chosen value
Say what makes that argument a proof and a set of protractor readings not one
Give two reasons a measured linear pair may fail to total 180° on the page

Where it usually goes wrong

"Vertically opposite means one is above the other." Fig. 5.3 breaks this on the same page the term is introduced: its vertically opposite pair ∠a and ∠c sit to the left and right of the vertex, level with each other. Checked against p.108. The word points at the vertex, not at the vertical direction — say so out loud when the term first appears.
"Four angles, so four different sizes." Only two sizes can appear, and they are forced as soon as one of them is fixed. Section 5 should show the fourth value arriving with no new information used.
"The pattern is true because I measured four pairs and it worked." Activity 1 produces evidence, not a reason. The chapter deliberately puts the letters argument after the measuring, and then names the difference. An explanation that stops at the measuring has taught the opposite of the section.
"My protractor said 179°, so the rule is only roughly true." The chapter reverses this: the reasoning is exact and the drawing is approximate. The ideal, thickness-free line is a decision about what is being reasoned about, not a fudge.
"If two of these four are equal, the lines must be perpendicular." Every crossing already has two equal pairs. Equal neighbours is the extra condition, and that is the next topic.
"Linear pairs add to 180° because the book says so." They add to 180° because their two outer arms together make one straight line, and a straight line makes a straight angle. Show the two arms sweeping into a line.

Questions to check understanding

Given one angle at a crossing, state the other three and give a reason for each
List every linear pair and every pair of vertically opposite angles in a lettered figure (the printed table on p.108 is exactly this task)
Explain, without measuring, why the two angles of a linear pair add to 180°
Say why two vertically opposite angles must be equal, using letters and not a chosen value
Given a measured pair that adds to 179°, say what has gone wrong and where
Decide whether a stated relation ("these two are equal") holds for any crossing or only for the one drawn
Multi-step items later in the chapter (the Figure it Out, pp.123–125, which opens with Fig. 5.30 on p.123) all begin with this step, so it is examined indirectly throughout the chapter's exercise set

Examples worth working on the board

Fig. 5.1 (Part I, p.106). Checked against the printed page. A square outline with dashed creases across it: the two mid-lines, both diagonals, and further quarter creases — a picture of many crossings and many near-parallels at once. Redraw it; do not lift it. It is the visual question the whole chapter answers.
Fig. 5.2 (Part I, p.107). Checked against the printed page. Line l is drawn horizontal with arrowheads at both ends; line m crosses it running from lower left to upper right. The four angles are lettered clockwise from the top left: ∠a upper left, ∠b upper right, ∠c lower right, ∠d lower left. In the printed figure ∠a and ∠c carry red arcs, so the equal pair is already hinted at graphically before it is argued.
The numeric walk (Part I, §5.1, p.107). Input: ∠a = 120°. The chapter walks ∠a → ∠b → ∠c → ∠d, using at each step that the two angles named form a straight angle.
The general argument (Part I, §5.1, p.107). Inputs, with no number chosen: ∠a + ∠b = 180° along one line, ∠a + ∠d = 180° along the other, so ∠b = ∠d; and ∠b + ∠a = 180° with ∠b + ∠c = 180°, so ∠a = ∠c. This is the passage.
Fig. 5.3 (Part I, p.108). Checked against the printed page. Lines l and m cross in a narrow X. The labels sit at the four compass points of the crossing: ∠a to the left, ∠b at the top, ∠c to the right, ∠d at the bottom. So the vertically opposite pairs here are ∠a with ∠c — side by side on the page — and ∠b with ∠d. The printed table has two rows, one headed for linear pairs and one for the opposite pairs, each started with a single example and then left open. There are four linear pairs (a-b, b-c, c-d, d-a) and two opposite pairs (a-c, b-d); the solutions appendix bound after the chapter in the cached PDF confirms exactly this list.
Why measurements miss (Part I, "Measurements and Geometry", p.108). Two causes are printed: a protractor used badly, and drawn lines having a thickness that an ideal line does not. The section's closing point is that the predicted and the measured values still come out close, which is why geometry is used in physics, art, engineering and architecture.

Figures to have open

One crossing of two lines, redrawn, that can carry four lettered arcs and be re-lettered between the Fig. 5.2 arrangement (a, b, c, d clockwise from upper left) and the Fig. 5.3 arrangement (a, b, c, d at left, top, right, bottom). Standard schematic, but the two letterings must match the printed ones, because the Fig. 5.3 lettering is what defeats the "vertically = above" misreading.
A folded square with creases, for section 1. Redraw; Fig. 5.1 is the book's own artwork.
A protractor overlay that can be laid on a drawn angle and read, for sections 4 and 11.
A thick-stroke line beside a hairline, at high magnification, for section 11.
No photograph or data table from the textbook is needed.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part I, printed Chapter 5 "Parallel and Intersecting Lines", §5.1 "Across the Line", pp.106–108 — the folded-square opening and Fig. 5.1 (p.106), Fig. 5.2 with Activity 1 and the 120° walk and the lettered generalisation (p.107), the naming of vertically opposite angles and of proof, and the Figure it Out table with Fig. 5.3 (p.108)
Same part, the unnumbered block "Measurements and Geometry", p.108, sitting between §5.1 and §5.2
Same part, SUMMARY, p.126, first bullet, for the chapter's own compressed statement of this result
Solutions appendix bound after p.126 in the cached PDF (not part of the printed book), for the completed Fig. 5.3 table