SAT Math — polygon angle sums and regular polygons

Polygons on the SAT sit inside the lines, angles and triangles skill of the Geometry and Trigonometry domain. The College Board's framework names the triangle angle sum theorem and the angles formed by parallel lines, and polygon questions are built from exactly those tools: any polygon splits into triangles from one vertex, and a parallelogram's angles come from parallel sides. The formulas themselves are short, but the reference sheet in the testing app gives only the triangle's 180 degrees, so the polygon versions have to be known or rebuilt on the spot. This material practices both.

The twelve quiz questions move from the sum of the interior angles, (n − 2) · 180°, to the sum of the exterior angles, which is always 360° for a convex polygon, and then to regular polygons, where every angle is equal. Students find the missing angle of a pentagon, the number of sides of a regular polygon from an interior angle of 140° and from an exterior angle of 24°, the interior angle of a regular octagon, and a missing exterior angle. Algebra enters through a hexagon whose angles are 2x, 2x, 3x, 3x, 4x and 4x degrees, a regular polygon whose interior angle is four times its exterior angle, and two regular polygons with n and 2n sides whose angles differ by 20°. A parallelogram with angle expressions checks the difference between consecutive and opposite angles.

Two questions go inside the figure: the area of a regular hexagon, found by splitting it into six equilateral triangles and written as a multiple of √3, and the angle a diagonal makes with a side of a regular pentagon, which comes from an isosceles triangle. The last question asks which regular polygon, in two copies, fits around a point with a square.

Seven questions have a drawing built from the stated angles, so every figure matches its numbers, with the unknown marked but not labeled. Every question also states all its information in words. The explanations name the common confusions behind the wrong options: interior and exterior angles swapped, the number of sides confused with n − 2, the hexagon's angle sum used for a pentagon, the exterior angle reported as a count of sides, and consecutive angles treated as equal.

The flashcards give the angle-sum formulas, the exterior angle of a regular polygon, the link between interior and exterior angles, the regular hexagon's area, the angle facts of a parallelogram and the rule for polygons meeting at a point.

The material offers a quiz and flashcards. It is practice written by Zestly and is not affiliated with or endorsed by the College Board.

• Use (n − 2) · 180° for interior angle sums and 360° for exterior angle sums
• Find the number of sides of a regular polygon from an interior or exterior angle
• Solve polygon angle problems with algebraic angle measures
• Find the area of a regular hexagon and angles formed by a diagonal of a regular pentagon
• Apply the angle facts of parallelograms and of polygons meeting at a point

Practice material written by Zestly, based on the College Board Assessment Framework for the Digital SAT Suite (version 3.01, August 2024), Geometry and Trigonometry domain, skill Lines, angles, and triangles (triangle angle sum, parallel lines) extended to polygons.