Find the sum of the interior angles of a 10-gon.
Unit 07 · Lesson 01 · Polygons & Quadrilaterals
Interior and Exterior Angles of Polygons
Derive and apply polygon interior-angle sums and the constant exterior-angle sum.
Learning intention
Use accurate diagrams, definitions, measurements, and reasoning to derive and apply polygon interior-angle sums and the constant exterior-angle sum.
Success evidence
- Label the figure and units before calculating.
- Select and justify the governing definition, theorem, relationship, or construction.
- Show enough work that another learner can audit the conclusion.
- Check the result against the diagram, scale, and stated constraints.
Visual model
Classify polygons and quadrilaterals using angle sums, side relationships, diagonals, symmetry, and coordinate evidence.
S=(n-2)180^\circE=360^\circA=\frac12 aP
Worked reasoning
Process: List the properties required by the classification, calculate or prove each one, then state the most specific valid name.
- Read the figure and rewrite all given information with correct notation.
- Identify the exact relationship that connects the known and unknown quantities.
- Substitute, construct, or prove one justified step at a time.
- State the result with units and a sentence explaining what it means.
Misconception check: A square belongs to both the rectangle and rhombus families; classifications are hierarchical rather than mutually exclusive.
Khaemenes Academy · Open-Age Geometry
Interior and Exterior Angles of Polygons
Find, construct, prove, or explain each result. Show reasoning and label units.
Name
Date
Find each exterior angle of a regular 10-gon.
Which quadrilateral has four congruent sides and four right angles?
What do the diagonals of a parallelogram do?
What additional property turns a parallelogram into a rectangle?
A regular polygon has perimeter 48 and apothem 7. Find its area.