Angle Sum of a Quadrilateral

A diagonal splits any quadrilateral into two triangles, so its four angles add to \(2 \times 180^\circ = 360^\circ\). This NSW Year 7 maths subtopic (NESA outcome MA4‑GEO‑C‑01) uses that angle sum to find unknown angles.

You will find a missing angle by subtracting the known angles from \(360^\circ\), include the reflex angle in a non-convex shape, use equal opposite angles in a parallelogram and the symmetry of kites and isosceles trapeziums, and solve equations such as \(x + 2x + 3x + 4x = 360\). Checking the corners of a garden bed is a real use. It is part of Year 7 Geometry.