Skip to content

Quiz: Polygons and Quadrilaterals

Test your understanding of polygon angle formulas, quadrilateral classifications, and their properties with these questions.

1. A polygon with 8 sides is called:

  1. Hexagon
  2. Pentagon
  3. Octagon
  4. Decagon
Show Answer

The correct answer is C. An octagon is a polygon with 8 sides. The prefix "octa-" means eight (think of "octopus" with 8 tentacles). A hexagon (A) has 6 sides, a pentagon (B) has 5 sides, and a decagon (D) has 10 sides. Octagons are commonly seen as stop signs.

Concept Tested: Polygon Classification

See: Chapter 9: Polygon Classification

2. What is the sum of the interior angles of ANY quadrilateral?

  1. 180°
  2. 270°
  3. 360°
  4. 540°
Show Answer

The correct answer is C. The interior angle sum for any polygon is (n-2) × 180°, where n is the number of sides. For a quadrilateral, n = 4, so the sum is (4-2) × 180° = 2 × 180° = 360°. This holds true for all quadrilaterals—squares, rectangles, parallelograms, trapezoids, kites, and even irregular quadrilaterals. Option A (180°) is the angle sum for a triangle. Option D (540°) is the angle sum for a pentagon.

Concept Tested: Interior Angle Sum of Polygons

See: Chapter 9: Interior Angles of Polygons

3. In any convex polygon, the sum of the exterior angles (one at each vertex) is always:

  1. 180°
  2. 360°
  3. It depends on the number of sides
  4. 90°
Show Answer

The correct answer is B. The sum of exterior angles of any convex polygon is always 360°, regardless of the number of sides. This makes sense if you imagine walking around the perimeter—you make one complete rotation (360°) by the time you return to your starting point. This constant sum is a beautiful property that applies to triangles, quadrilaterals, pentagons, and all other polygons.

Concept Tested: Exterior Angle Sum

See: Chapter 9: Exterior Angles of Polygons

4. A quadrilateral with exactly one pair of parallel sides is called:

  1. Parallelogram
  2. Trapezoid
  3. Rhombus
  4. Kite
Show Answer

The correct answer is B. A trapezoid is defined as a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. A parallelogram (A) has two pairs of parallel sides. A rhombus (C) is a special parallelogram with all sides equal. A kite (D) has two pairs of consecutive equal sides but no parallel sides.

Concept Tested: Trapezoid Definition

See: Chapter 9: Quadrilaterals

  1. They are both special types of parallelograms
  2. A rectangle is a parallelogram, but a rhombus is not
  3. A rhombus is a parallelogram, but a rectangle is not
  4. Neither is a type of parallelogram
Show Answer

The correct answer is A. Both rectangles and rhombuses are special types of parallelograms. A rectangle is a parallelogram with four right angles. A rhombus is a parallelogram with four equal sides. Because they are parallelograms, they both have all the properties of parallelograms (opposite sides parallel, opposite sides equal, opposite angles equal, consecutive angles supplementary, diagonals bisect each other) plus their own special properties.

Concept Tested: Quadrilateral Hierarchy

See: Chapter 9: Quadrilateral Family Hierarchy

6. What special property distinguishes a square from other rectangles?

  1. A square has four right angles
  2. A square has all four sides equal
  3. A square has parallel opposite sides
  4. A square has diagonals that bisect each other
Show Answer

The correct answer is B. While all rectangles have four right angles (A), parallel opposite sides (C), and diagonals that bisect each other (D), a square is the special rectangle that also has all four sides equal in length. In fact, a square is both a rectangle (four right angles) AND a rhombus (four equal sides), making it the most special quadrilateral.

Concept Tested: Square Properties

See: Chapter 9: Quadrilateral Hierarchy

7. What is the sum of the interior angles of a hexagon?

  1. 540°
  2. 720°
  3. 900°
  4. 1080°
Show Answer

The correct answer is B. Using the interior angle sum formula S = (n-2) × 180°, where n = 6 for a hexagon: S = (6-2) × 180° = 4 × 180° = 720°. A hexagon can be divided into 4 triangles from one vertex, and since each triangle has 180° of angles, the total is 4 × 180° = 720°. Option A (540°) is for a pentagon, option D (1080°) is for an octagon.

Concept Tested: Interior Angle Sum Application

See: Chapter 9: Interior Angle Sum Formula

8. Each interior angle of a regular pentagon measures:

  1. 72°
  2. 90°
  3. 108°
  4. 120°
Show Answer

The correct answer is C. For a regular pentagon (n = 5), each interior angle = (n-2) × 180° / n = (5-2) × 180° / 5 = 3 × 180° / 5 = 540° / 5 = 108°. Since a regular pentagon has all angles equal, we divide the total interior angle sum (540°) by the number of angles (5) to get 108° for each angle. Option A (72°) is each exterior angle of a regular pentagon.

Concept Tested: Regular Polygon Interior Angles

See: Chapter 9: Each Interior Angle in Regular Polygon

9. A parallelogram has opposite angles that are:

  1. Complementary (sum to 90°)
  2. Supplementary (sum to 180°)
  3. Congruent (equal)
  4. Right angles (90° each)
Show Answer

The correct answer is C. In a parallelogram, opposite angles are congruent (equal in measure). This means if angle A measures 70°, then angle C (opposite to A) also measures 70°. Note that consecutive angles in a parallelogram are supplementary (sum to 180°), not opposite angles. Option B would be correct if it said "consecutive angles." Options A and D describe special cases that don't apply to all parallelograms.

Concept Tested: Parallelogram Properties

See: Chapter 9: Parallelograms

10. A square has all the properties of which of the following quadrilaterals?

  1. Only rectangles
  2. Only rhombuses
  3. Both rectangles and rhombuses
  4. Trapezoids
Show Answer

The correct answer is C. A square is both a rectangle (it has four right angles) and a rhombus (it has four equal sides). Therefore, it inherits ALL the properties of both figures. From rectangles, it gets: four right angles and congruent diagonals. From rhombuses, it gets: four equal sides and perpendicular diagonals. A square is the only quadrilateral that belongs to both families, sitting at the bottom of the quadrilateral hierarchy as the most special quadrilateral. Option D is incorrect because squares have two pairs of parallel sides, not just one.

Concept Tested: Square as Intersection of Rectangle and Rhombus

See: Chapter 9: Quadrilateral Family Hierarchy

Score

Check your answers above. How did you do?

  • 9-10 correct: Excellent! You have mastered polygons and quadrilateral classifications.
  • 7-8 correct: Good work! Review the angle formulas and quadrilateral hierarchy.
  • 5-6 correct: Study polygon angle sums and the properties of special quadrilaterals.
  • Below 5: Review the chapter carefully, especially interior/exterior angle formulas and quadrilateral definitions.