Alternate angles, and interior angles that add to 180°

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What to assume they know

Corresponding angles are equal exactly when the lines are parallel: corresponding angles are equal exactly when the two lines are parallel
The four angles at a crossing: vertically opposite and linear pairs: vertically opposite angles are equal; linear pairs total 180°
A transversal creates two matching sets of four angles: the eight angles a transversal makes, and how to navigate between them
Subtracting from 180 accurately, and chaining two or three such steps
Reading a lettered or numbered figure and holding the labels straight

What they should be able to do

Identify the alternate angle of a named angle in a transversal figure
Find an alternate angle in two steps — corresponding, then vertically opposite — and say which fact each step used
State the condition under which alternate angles are equal, and not state it without the condition
Identify the interior angles on one side of the transversal
Show that same-side interior angles total 180°, by composing a corresponding angle with a linear pair
Given one of the eight angles at a pair of parallel lines, find the other seven
Use unequal corresponding angles to establish that two lines are not parallel
Handle a figure with two independent pairs of parallel lines, applying the interior-angle result twice

Where it usually goes wrong

"Alternate angles are equal." Only across parallel lines. This is the chapter's most dangerous half-sentence, and the danger is real here: the printed wording inside Activity 6 says the equality holds irrespective of the measure of the starting angle, which is true, but it holds because the corresponding-angle step is available, and that step needs parallelism. The boxed statement on p.120 states the condition properly.
"Interior angles are equal, like the other pairs." They total 180°. They are equal only in the special case where the transversal meets the parallels at 90°, and then both are 90°. Say that case out loud; a student who has met only perpendicular examples will generalise the wrong way.
"Alternate means the two angles are next to each other." They sit on opposite sides of the transversal, one at each crossing, both between the two lines. Show a wrong pick beside the right one on Fig. 5.25's lettering.
"There are four separate rules to memorise here." There are two facts and two compositions. Section 4 and section 9 should be built as the same move with a different second step.
"Alternate angles are a new fact, so they need a new proof." The chapter derives them and says so — it points out that no measurement was used. That sentence is the point of the section, not a flourish.
"If two angles at a transversal are supplementary, the lines must be parallel." Only for the interior pair on one side. Any linear pair at either crossing is already supplementary whatever the lines do.
"Example 4 needs a rule about parallelograms." It does not, and the chapter does not use one. It applies the interior-angle result twice, once to each pair of parallel sides.

Questions to check understanding

Name the angle alternate to a stated one, in a lettered figure
Given one of the eight angles at a pair of parallel lines, find the other seven
Justify the equality of an alternate pair using two earlier facts, without measuring
Given two same-side interior angles, one known, find the other
Given two angles at a transversal, decide whether the two lines are parallel
Chase an angle through two or three steps in a compound figure (this is Q1 and Q2 of the printed exercise set, pp.123–124)
Solve a figure with two transversals through one point (Q4, Fig. 5.33, p.124)
Add an auxiliary parallel line to make a zigzag solvable (Q6, Fig. 5.35, p.125, which prints the hint)
Say which of two named angle pairs is equal and which totals 180°, and why the answers differ

Examples worth working on the board

Fig. 5.25 (Part I, §5.8, p.120). Checked against the printed page. Two lines l above and m below, both sloping gently down to the right at the same slope, cut by a steep transversal t that runs from upper left down to lower right. Eight lettered angles: at the upper crossing a is upper left, b upper right, d lower left, c lower right; at the lower crossing e is upper left, f upper right, h lower left, g lower right. The printed alternate pairs are ∠d with ∠f, and ∠c with ∠e. Note a subtlety in the drawing: l and m are drawn as a parallel pair but carry no arrow marks saying so — the only marks on them are the arrowheads that show the lines continue. The boxed result and Activity 6 both need the parallelism. Redraw the lettering exactly otherwise; the whole of §5.8 refers back to it.
The two-hop route (Part I, §5.8, p.120). Input: to reach the alternate angle of ∠f, first go to its corresponding angle ∠b at the other crossing, then to ∠b's vertically opposite angle ∠d.
Activity 6 (Part I, §5.8, p.120). Input: ∠f = 120°. Then let it repeat the argument with the number removed, which is what the printed text does next.
Example 1 (Part I, §5.8; question on p.120, Fig. 5.26 and solution on p.121). Checked against the printed page. In Fig. 5.26 the two parallel lines l and m both slope up to the right and each carries a single-arrow parallel mark; the transversal t runs from upper left down to lower right, crossing l first and m second. At the first crossing the numbering is 1 left, 2 top, 3 right, 4 bottom; at the second, 5 left, 6 top, 7 right, 8 bottom. Input: ∠6 = 135°.
Example 2 (Part I, §5.8, p.121). Checked against the printed page. Fig. 5.27 has the same lettering scheme as Fig. 5.25, but l and m carry no parallel marks and are not drawn parallel. Inputs: ∠a = 120° and ∠f = 70°. The route is: ∠a sits beside ∠b along one line, so the two total 180°; ∠b then matches ∠f across the transversal.
Example 3 (Part I, §5.8; question and Fig. 5.28 on p.121, solution on p.122). Checked against the printed page. Fig. 5.28 has l and m drawn horizontal and parallel, and t running from upper left to lower right. At the l crossing, 1 is upper left, 2 upper right, 4 lower left, 3 lower right; at the m crossing, 5 upper left, 6 upper right, 8 lower left, 7 lower right. Input: ∠3 = 50°. Route: ∠2 and ∠3 are a linear pair; ∠2 and ∠6 are the corresponding pair. The chapter then names ∠3 and ∠6 as interior angles.
The interior-angle result (Part I, §5.8, p.122). The chapter does not state it and then illustrate it. It sets the reader to try several values of ∠3, look at the resulting ∠6, find the relation and then justify it — and only after that is the total of 180° written down, inside a tinted box. Keep that order.
Example 4 (Part I, §5.8, p.122). Checked against the printed page. Fig. 5.29 is a parallelogram lettered A top left, B top right, C bottom right, D bottom left, with the diagonal AC drawn in; AB and DC carry parallel arrow marks and so do AD and BC. Inputs: ∠DAC = 65° and ∠ADC = 60°. The three angles asked for are ∠CAB, ∠ABC and ∠BCD. Route: AD is a transversal to the parallel pair AB and DC, giving ∠ADC + ∠DAB = 180°; then ∠DAB splits into ∠DAC and ∠CAB; then DC is a transversal to the parallel pair AD and BC, giving ∠ADC + ∠BCD = 180°. A good internal check for the figure is that the four angles of the parallelogram must total 360°.
The exercise set (Part I, Figure it Out, §5.8, pp.123–125). Checked against the printed page. Six questions. Q1 (Fig. 5.30, p.123) is ten small transversal figures lettered a to j, each with one or more measures given and one blank to fill; the later ones need two or three chained steps. Q2 (Fig. 5.31, p.124) is four figures, each asking for a single angle a from two or three givens, and one of them combines a right angle with a pair of parallels. Q3 (Fig. 5.32, p.124) asks for x and y in two figures. Q4 (Fig. 5.33, p.124) puts two transversals through one point on the lower of two parallel lines, and asks for three angles at that point — a useful check for the figure is that those three must total 180°. Q5 (Fig. 5.34, p.125) has three parallel lines and one perpendicular, and asks for two angles. Q6 (Fig. 5.35, p.125) is a zigzag with four marked angles and prints a hint telling the reader to draw auxiliary parallels through two of the corners. The solutions appendix bound after the chapter carries answers for all six; they are not part of the printed chapter.

Figures to have open

Fig. 5.25 redrawn with its printed lettering, able to be shown moving so that a highlight can travel from one angle to its corresponding angle and then to its vertically opposite one. This is the topic's central figure.
A transversal-and-parallels figure whose transversal angle can be dragged, with all eight measures updating live. It carries sections 5, 6 and 9 and shows that only two values ever appear.
The Example 4 parallelogram with its diagonal and both pairs of parallel marks, matching Fig. 5.29.
A single summary diagram naming all four pairs — corresponding, alternate, interior on the same side, vertically opposite — on one figure. The chapter has no such diagram; it names each pair on its own page.
No photograph, table or dataset 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", §5.8 "Alternate Angles", pp.120–125 — the naming and Fig. 5.25, Activity 6, the general argument and the boxed result (p.120); Fig. 5.26 with Example 1's solution, Example 2 with Fig. 5.27, and Example 3's question with Fig. 5.28 (p.121); Example 3's solution, the naming of interior angles, the boxed exploration prompt and Example 4 with Fig. 5.29 (p.122); the Figure it Out with Figs. 5.30 to 5.35 (pp.123–125)
Same part, §5.6, pp.115–118, and §5.1, pp.107–108, for the two facts every result here is composed from
Same part, SUMMARY, p.126, sixth and seventh bullets
Solutions appendix bound after p.126 in the cached PDF (not part of the printed book), for the answers to the six exercise questions