My 7th-grade daughter is doing geometry
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My 7th-grade daughter is doing geometry homework tonight on triangles.
The problem shows a triangle with interior angles 40° and 70°, and asks for the exterior angle at the third vertex.
She calculated 180° - 40° - 70° = 70°, and then stopped and wrote 70° as the final exterior angle (confusing the third interior angle with the exterior angle on the straight line).
Could you guide me on:
1. The exact name of this misconception (confusing adjacent interior angle with exterior angle / straight-line supplement).
2. 1-2 Socratic diagnostic questions I can ask her tonight with a physical straight-line visual clue, and how I'll know she clicked.
3. One parallel changed-number practice problem without spoiling any answers.
4. One single clarifying question placed at the very end.
Answer
**The name (say it out loud as you sit down):**
"Interior–exterior confusion at the same vertex" — she's calling the angle *inside* the triangle the "outside" one. The exterior angle is the one that sits on the straight line, *outside* the triangle, not the corner she just summed to.
**Two Socratic questions with a straight-line visual** (use a pencil or ruler on the page):
**Q1.** Lay your pencil along one of the two sides meeting at the third vertex, then slide it past that vertex until the pencil makes a straight line. Now point: how many angles are sitting at that vertex on the pencil-line, and which one is *outside* the triangle?"
> **How you'll know it clicked:** She points to the angle between the extended pencil and the *other* triangle side — the one not enclosed by the triangle. If she still points inside the triangle, interior and exterior haven't separated for her yet; redraw the line and ask again.
**Q2.** "Those two angles at the vertex — the inside one and the outside one — sit on a straight line. What's that straight line worth? So if the inside angle is 70°, what does the outside one have to be?"
> **How you'll know it clicked:** She says "180°" out loud, then subtracts to get the outside angle on her own. The number she lands on is hers to say — yours to listen for, not to supply.
**One parallel changed-number item** (no answer from you — she does both parts):
A triangle has interior angles 35° and 85°.
(a) Find the third interior angle.
(b) Find the exterior angle at that same vertex.
(If she'll draw the straight-line extension first, that's the right move.)
**One clarifying question for tonight:**
On her worksheet, is the exterior angle already drawn on the figure (an arc sticking out from the third vertex), or does she have to extend a side herself?