Geometry: Angles, Polygons and Circles

Angle facts, polygon angles, similarity and congruence, and the circle theorems — each with the reason it holds rather than as a list to memorise.

หลักสูตรแกนกลาง / สสวท.: การวัดและเรขาคณิต (Geometry and Measure)ครอบคลุม ม.2 บทที่ 8-10 · ม.3 บทที่ 4 ความคล้าย และบทที่ 7 วงกลม
Common Core (US): 8.G, G-C, G-SRT
Cambridge: IGCSE 0580 — Topic 4: Geometry (Core and Extended)

7.1 Angle and polygon facts

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The facts you may quote by name
- angles on a straight line: $18 0^{\circ}$ ; around a point: $36 0^{\circ}$
- vertically opposite angles are equal
- on parallel lines: corresponding and alternate angles are equal; co-interior angles add to $18 0^{\circ}$
- triangle: $18 0^{\circ}$ ; quadrilateral: $36 0^{\circ}$
- polygon interior sum: $(n - 2) \times 18 0^{\circ}$ ; exterior sum: always $36 0^{\circ}$

เคล็ดลับ

For a regular polygon, go via the exterior angle: $360 \div n$ gives it, and $180$ minus that gives the interior. Fewer steps than the interior-sum formula and fewer places to slip.

ข้อควรระวัง

Every angle answer needs its reason written beside it. Diagrams are not to scale, and "it looks about right" earns nothing — the reason is what is being marked.

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The whole chapter is written; we read it back section by section before releasing it, because maths nobody has checked should not be on a public page. What is open is complete — nothing here is abridged.

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