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
Share and support
Teaching Table
Set out your lesson
“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?”
Full guide and materials
- Activity. 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
What to notice. 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
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
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?
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
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Learning resources
External links for extra practice. They do not replace Gakuva’s teaching approach.
No additional resources are listed for this topic.
The teaching approach appears above.
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