Angle Sum of Triangles and Quadrilaterals

The angles of a triangle add to \(180^\circ\) and the angles of a quadrilateral add to \(360^\circ\), because a diagonal splits a quadrilateral into two triangles. This NSW Year 8 maths subtopic (NESA outcome MA4‑GEO‑C‑01) also uses the exterior angle of a triangle, which is the same size as the two opposite interior angles added together.

You will solve for angles given as expressions, including isosceles triangles and pronumerals on both sides, find corners made of two parts, and share an angle sum in a ratio such as \(2 : 3 : 4\). You will also work with non-convex quadrilaterals, decide whether a set of angles is possible, and find the corners of a farmer's paddock. It is part of Year 8 Geometry.