IGCSE›Edexcel IGCSE Maths›Mind mapsAngles in Polygons & Parallel LinesEdexcel IGCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsBasic factsAngles on a line sum to 180∘180^{\circ}180∘Angles around a point sum to 360∘360^{\circ}360∘Vertically opposite angles are equalParallel linesCorresponding angles are equal (F)Alternate angles are equal (Z)Co-interior angles sum to 180∘180^{\circ}180∘ (C)Only valid if lines are parallelAngle rulespolygons and parallel lines180∘180^{\circ}180∘360∘360^{\circ}360∘Interior anglesSum =(n−2)×180∘= (n-2) \times 180^{\circ}=(n−2)×180∘Splits into n−2n - 2n−2 trianglesRegular polygon: divide the sum by nHexagon: 720∘÷6=720^{\circ} \div 6 = 720∘÷6= 120°Exterior anglesExterior angles always sum to 360∘360^{\circ}360∘Regular polygon: 360∘n\frac{360^{\circ}}{n}n360∘Interior + exterior =180∘= 180^{\circ}=180∘Number of sides: n=360∘÷n = 360^{\circ} \divn=360∘÷ exterior angleExam tipsName the rule at each step for method marksMark known angles on the diagram firstDo not assume all four angles at a crossing are equalDo not mix up the 360° and (n−2)×180∘(n-2) \times 180^{\circ}(n−2)×180∘ sums