Constructing from two angles and the side between them

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What to assume they know

Constructing from two sides and the angle between them — constructing from two sides and their included angle
Drawing an angle of a stated size at a given point on a given ray
Alternate angles, and interior angles that add to 180° and Part I, Chapter 5 generally: parallel lines cut by a transversal, and that the two interior angles on one side of the transversal total 180°
Recognising a right angle, and comparing an angle with 90°
Adding two angle measures and comparing the total with 180°

What they should be able to do

Identify which side is included between two named angles of a triangle
Construct a triangle from two angles and their included side
Explain why two base angles that are each at least 90° cannot produce a triangle
Explain why the two arms cease to meet exactly when they become parallel
Use the transversal rule to obtain the boundary value of the second angle for a given first angle
State the existence condition as a requirement on what the two given angles total
Decide for a given pair of angles whether a triangle exists, and give the totalling that decides it
Argue that the included sidelength plays no part in whether the triangle exists
Observe that fixing two angles fixes the third, whatever the included side

Where it usually goes wrong

"A longer base gives the arms more room to meet." The chapter kills this explicitly on p.163. Lengthening the base slides the two arms apart but tilts neither, so a pair that meets still meets and a pair that misses still misses. The figure in section 10 has to make that visible.
"If one of the two angles is 90°, there is no triangle." 90° with 85° works — their total is under 180°. The failure needs both angles to be at least 90°, or one large enough to make up the difference. The printed pair on p.163 is there to catch exactly this error.
"The two arms are parallel, so that is the case where they meet at the very last moment." Parallel arms do not meet at all. The parallel position is the first arrangement that fails, and the chapter's phrasing puts it on the failing side: at 140° and above there is no triangle. Get the inequality the right way round.
"Two angles are not enough to pin a triangle down." They pin its shape down completely, and the third angle with it — as section 12 shows. What they do not pin down is its size. That distinction is worth naming even though this chapter does not.
"Failing means the arms cross on the wrong side of the base." In the chapter's picture the arms are drawn upward from the base and either meet above it or never meet. Extending them backwards is a different figure and not what is being constructed.
"The rule must involve all three angles." The test uses only the two given ones. That is what makes it usable before any third angle exists.

Questions to check understanding

Construct a triangle from two angles and their included side (the three sets on p.162 are exactly this task)
Given a pair of angles, decide whether a triangle exists and show the totalling
Given one angle, supply partners that do and do not admit a triangle, with a reason (the four-angle exercise on p.163)
Explain why the included sidelength does not affect existence
Explain what happens to the two arms at the exact boundary value
Given two angles of a triangle, state the third — the natural follow-on, and the subject of Why the three angles of any triangle add to 180°
Identify the included side between two named angles of a labelled triangle

Examples worth working on the board

The three specimen figures (Part I, §7.3, p.161). Checked against the printed page. Three triangles with two angles and one side marked on each: 40° and 50° at the two ends of a 5 cm base; 30° and 45° at the two ends of a 4 cm base; and a narrow one with 20° at the top, 6 cm down its right side and 50° at the bottom. The third is the useful one — the given side is not horizontal and not at the bottom, so the student has to work out which side is included rather than assume it.
The worked construction (Part I, §7.3, p.161). Inputs: AB = 5 cm, ∠A = 45°, ∠B = 80°. Two figures: a small finished triangle with C at the top, and a larger in-progress one showing the two arms drawn out from A and B and crossing at C.
The obvious failures (Part I, §7.3, p.162). Checked against the printed page. Three pairs of rays are drawn on short base segments, with no angle values written on. In the first pair both arms lean outwards. In the second one arm is square to the base and the other leans out. In the third both arms are square to the base — the two square corners are marked.
The 40° experiment (Part I, §7.3, pp.162–163). Checked against the printed page. On p.162 the base AB is drawn with a 40° arm from A, labelled l, running up to C. On p.163 the same figure reappears with a fan of four arms drawn from B leaning progressively further right, the innermost of which is drawn in blue. Inputs: the fixed 40° at A, and the fan. What the blue arm is, and what ∠B measures there, is what the explanation derives.
The transversal step (Part I, §7.3, p.163). Inputs: the two arms are parallel; AB cuts across both; the two angles at A and B lie inside the pair and on the same side of AB. The rule that they total 180° is the one recalled from the parallel-lines chapter.
The conclusion about the base (Part I, §7.3, p.163). The chapter states outright that the length AB has no bearing on whether a triangle exists. This is a strong claim and it is printed; do not soften it into "has little effect".
The angle pairs to sort (Part I, §7.3, p.163). 35° and 150° · 70° and 30° · 90° and 85° · 50° and 150°. The third pair is the instructive one — it contains a right angle and still works, which blocks the reading that "90° in the list means no triangle".
The first-angle exercise (Part I, §7.3, p.163). For each of 30°, 70°, 54° and 144°, the student must supply two partners that work and two that do not. Give the four starting angles as inputs.
The 60°, 70°, 5 cm case (Part I, §7.3, p.164). Inputs: two angles whose total is under 180°, an included side of 5 cm, and then the same two angles with a 7 cm side. The observation the chapter is steering at — that the third angle is unchanged — is the bridge into Why the three angles of any triangle add to 180° and should be left as an observation here, not proved.

Figures to have open

A base with two arms whose angles can be set independently and swung continuously, with the crossing point tracked as it slides out to infinity and vanishes at the parallel position. This movement carries sections 7, 8 and 10 and is the topic's central asset.
The same figure with a slider for the base length, so the base can be stretched while both angles hold. Section 10 fails without it.
A parallel pair cut by a transversal with the two interior angles on one side marked, matching the Part I, Chapter 5 convention this book already used.
The three failing configurations from p.162, redrawn with their arms extended much further than the printed figure does.
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 7 "A Tale of Three Intersecting Lines", §7.3 "Construction of Triangles When Some Sides and Angles are Given" — the bold unnumbered block "Two Angles and the Included Side", pp.161–164
Within it: the specimen figures, the worked ∆ABC and its three steps, p.161; the Figure it Out set, the bold unnumbered block "Do triangles always exist?", the three failing configurations and the 40° figure, p.162; the fan of arms with the blue limiting arm, the transversal step, the 140° boundary, the claim about the base length and the two Figure it Out exercises, p.163; the rule in terms of a sum and the 60°/70° experiment, p.164
Same part, SUMMARY, p.171, fourth bullet (b) — the chapter's own listing of this construction
Backward pointer: Part I, printed Chapter 5 "Parallel and Intersecting Lines", for the transversal rule the 140° step depends on