Angle sums in triangles and polygons
Derive and use the angle sum in a triangle (180°), use it to deduce the angle sum in any polygon ((n−2) × 180°), and calculate interior and exterior angles of regular polygons
Lesson
Set out your lesson
“Angle sums in triangles and polygons means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Paper shapes or a ruler and pencil
- Shape or angle name cards
Extra for the adult
Worked example. A rectangle has four right angles. Naming the property is the check.
Optional challenge. For Angle sums in triangles and polygons, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Angle sums in triangles and polygons, not mastery.
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Teaching approaches
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1 approach
Angle sums in triangles and polygons means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Paper shapes or a ruler and pencil; Shape or angle name cards. 1. Say the goal of Angle sums in triangles and polygons in plain words once. 2. Adult traces or shows one shape/angle and names a key property. 3. Child measures or classifies three shapes/angles and names a property each time. 4. Fresh check: one fresh property name. Record and stop. Done: three correct property names with a sketch or measure. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
Family records and proof options
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Practice this concept
Start practiceAngle sums in triangles and polygons practice
Practice key ideas from Angle sums in triangles and polygons.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
PhET Interactive Simulations · Practice link — not the full lesson
Area Builder
Before you open · source notes
Area Builder supports hands-on exploration for Angle sums in triangles and polygons. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Area Builder.” External page; Gakuva does not copy, host, embed, or redistribute materials.
Unknown — link only
Check understanding
- Calculate a missing angle in a triangle by subtracting the known angles from 180°
- Find the sum of interior angles in a hexagon by dividing it into triangles
- Calculate each interior and exterior angle of a regular polygon given the number of sides
“If your child knows two angles of a triangle are 50° and 70°, can they work out the third? And can they figure out the angles inside a regular pentagon?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 11–14
Standards