Polygon angles
A standard method from Geometry and data basics: the steps and worked examples.
Steps
- Interior angle sum = (n − 2) × 180°.
- Each exterior angle of a regular n-sided polygon = 360° ÷ n.
- Interior + exterior = 180°.
Worked examples
Example 1: Polygon angles: each interior angle of a regular polygon is 144°. How many sides does it have?
exterior angle = 180° − 144° = 36°
n = 360° ÷ 36° = 10Example 2: Prove two triangles congruent: AB and CD cross at M, with AM = BM and CM = DM. Prove △AMC ≅ △BMD.
AM = BM (given)
∠AMC = ∠BMD (vert. opp. ∠s)
CM = DM (given)
∴ △AMC ≅ △BMD (SAS)The angle is between the two sides in both triangles, so this is SAS, not SSA.
For the whole topic, read Geometry and data basics: key points, common mistakes and how the DSE tests it.