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Quizzes > Mathematics

Polygon Test: Identify Shapes by Number of Sides

Quick, free geometry quiz on shape names by sides. Instant results.

Editorial: Review CompletedCreated By: Excellence Culinaire Joyeria GastronomicaUpdated Aug 27, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art collage of colorful polygons including triangles hexagons nonagons floating on a golden yellow background

This polygon test helps you identify and name polygons by their number of sides, from triangles to nonagons. Use it to check gaps before a test, compare convex and concave shapes, and build speed. Keep going with polygon practice, dive deeper on sides of a heptagon, or widen your review with a quick geometric shapes quiz.

What is the name for a polygon with three sides?
Quadrilateral
Hexagon
Pentagon
Triangle
A polygon with three sides is called a triangle. Triangles are the simplest class of polygons and have many unique properties in geometry. The sum of its interior angles always equals 180. .
How many sides does a heptagon have?
7
8
6
9
A heptagon is defined as a seven-sided polygon. It is less common than pentagons or hexagons but appears in various tiling and geometry problems. The prefix hepta- means seven in Greek. .
What name is given to a polygon that has nine sides?
Decagon
Dodecagon
Octagon
Nonagon
A nine-sided polygon is known as a nonagon. The prefix nona- or ennea- indicates nine in Latin and Greek respectively. Nonagons can be regular or irregular depending on side lengths and angles. .
What is the sum of the interior angles of a triangle?
270
360
90
180
In Euclidean geometry, the interior angles of any triangle always add up to 180 degrees. This property can be proved by drawing a line parallel to one side of the triangle. It is fundamental to many geometry proofs and constructions. .
How many diagonals does a quadrilateral have?
3
2
1
4
A quadrilateral has four sides, and the number of diagonals is given by n(n-3)/2 which gives 41/2=2. These two diagonals connect opposite vertices inside the shape. Diagonals help in dividing the quadrilateral into triangles for area calculations. .
In a regular hexagon, what is the measure of each interior angle?
150
120
135
90
A regular hexagon has all sides and angles equal. The measure of each interior angle is (n?2)180/n = (6?2)180/6 = 120. These angles sum to 720 across the six interior angles. .
How many sides does a pentagon have?
6
5
4
7
A pentagon is a five-sided polygon. The prefix penta- comes from the Greek word for five. Regular pentagons appear in nature and architecture frequently due to their symmetry. .
What is the name of a twelve-sided polygon?
Undecagon
Dodecagon
Decagon
Nonagon
A polygon with twelve sides is called a dodecagon. The prefix dodeca- originates from the Greek word for twelve. Regular dodecagons have interior angles of 150 each. .
What is the sum of the interior angles of a pentagon?
450
720
360
540
The sum of the interior angles of any n-sided polygon is (n?2)180. For a pentagon, that gives (5?2)180=540. This holds true for both regular and irregular pentagons. .
Which formula computes the number of diagonals in an n-sided polygon?
360/n
n(n-1)/2
n(n-3)/2
(n-2)180
The number of diagonals in an n-sided polygon is given by n(n?3)/2 because each vertex connects to n?3 other vertices and each diagonal is counted twice. This formula works for any convex or concave simple polygon. .
What is the measure of each exterior angle in a regular octagon?
90
60
45
30
In a regular polygon, each exterior angle is 360/n. For an octagon, n=8, so each exterior angle equals 360/8=45. The interior angle would then be 180?45=135. .
What is the sum of the exterior angles of any convex polygon?
Depends on the number of sides
180
540
360
The sum of the exterior angles, one at each vertex, of any convex polygon always equals 360, regardless of the number of sides. This fact follows from walking around the polygon and turning through each exterior angle to complete a full rotation. .
Calculate the sum of interior angles for a convex 15-sided polygon.
2700
2340
2160
1800
Using the formula (n?2)180, a 15-sided polygon has (15?2)180=13180=2340 as the total of its interior angles. This applies to convex forms of the polygon as well. The formula derives from partitioning the shape into triangles. .
How many lines of symmetry does a regular nonagon have?
10
9
7
8
A regular n-sided polygon has n lines of symmetry, each passing through a vertex and the midpoint of the opposite side. For a nonagon (n=9), there are therefore 9 lines of symmetry. This symmetry property is characteristic of all regular polygons. .
A regular polygon has each interior angle measuring 140. How many sides does it have?
9
8
10
7
For a regular n-gon, each interior angle is (n?2)180/n. Setting this equal to 140 gives (n?2)180=140n, leading to n=9 after solving. Thus, the polygon is a nonagon. .
If one exterior angle of a regular polygon is 30, how many sides does the polygon have?
8
15
12
10
The measure of each exterior angle in a regular polygon is 360/n. Setting 360/n=30 and solving gives n=12. Therefore, the polygon is a regular dodecagon. .
What is the sum of the interior angles of an icosagon?
3600
3060
3240
3420
An icosagon has 20 sides, and the sum of its interior angles is (n?2)180 = (20?2)180 = 3240. This holds for any simple 20-sided polygon. The result comes from dividing the shape into triangles from one vertex. .
How many diagonals are in a convex 13-sided polygon?
65
60
52
78
The number of diagonals in an n-sided polygon is n(n?3)/2. For n=13, this is 1310/2=65. Each diagonal connects two non-adjacent vertices exactly once. .
A polygon has an interior angle sum of 2160. How many sides does this polygon have?
14
15
12
13
Using the formula (n?2)180=2160, solving gives n?2=12 and n=14. Thus, the polygon has 14 sides. This calculation works for any simple polygon in Euclidean space. .
In a regular 14-gon, what is the measure of each interior angle?
156
154.29
152
150
Each interior angle of a regular n-gon is (n?2)180/n. For n=14, this equals 12180/14?154.2857, which rounds to 154.29. Regular polygons distribute angles evenly around the center. .
A convex polygon has exterior angles that alternate between 10 and 20. How many sides does this polygon have?
24
18
12
30
Alternating exterior angles of 10 and 20 add to 30 per pair. The sum of all exterior angles in a convex polygon is 360, so there must be 360/30=12 pairs, giving 24 sides. This relies on the polygon being convex and angles summing to 360. .
What is the measure of each exterior angle of a regular 45-sided polygon?
6
5
10
8
Each exterior angle of a regular polygon equals 360/n. For n=45, this is 360/45=8. This applies to any regular polygon regardless of the number of sides. .
In a regular polygon, the ratio of its interior angle to its exterior angle is 5:1. How many sides does it have?
15
12
8
10
Let the exterior angle be x and the interior angle be 5x, then x+5x=180 giving x=30. The number of sides n=360/x=360/30=12. Thus the polygon is a regular dodecagon. .
A convex polygon has an interior angle that is twice as large as its exterior angle. How many sides does the polygon have?
6
3
9
12
If the exterior angle is x and the interior angle is 2x, they sum to 180, so x+2x=180 gives x=60. The polygon has 360/60=6 sides, making it a hexagon. This relies on the polygon being convex so angles sum correctly. .
What is the Schlfli symbol for a regular star heptagon connecting every second vertex?
{7/2}
{7/5}
{7/4}
{7/3}
A regular star polygon that connects every second vertex of a heptagon is denoted by the Schlfli symbol {7/2}. The first number indicates vertices and the second indicates the step used in vertex connection. Other fractions represent different star patterns on 7 vertices. .
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Study Outcomes

  1. Identify Polygon Types -

    Recognize and name polygons by their number of sides - from triangles and squares to hexagons and nonagons - to accurately identify polygon shapes.

  2. Analyze Interior Angles -

    Calculate and compare the sum of interior angles using key formulas, reinforcing your understanding in this polygon properties quiz.

  3. Distinguish Regular vs. Irregular Polygons -

    Apply criteria for equal sides and angles to classify polygons as regular or irregular in various geometry quiz polygons scenarios.

  4. Classify Polygons by Attributes -

    Use side length, vertex arrangement, and symmetry to group and differentiate polygons quickly during timed polygon quiz questions.

  5. Evaluate Shape Characteristics -

    Assess and justify your reasoning when selecting the correct polygon name, sharpening decision-making skills in every polygon quiz challenge.

Cheat Sheet

  1. Polygon Naming by Side Count -

    Understanding how to identify polygon shapes starts with knowing their side-based names: triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), and so on up to nonagons (9 sides) and beyond. A handy mnemonic is "Tasty Quiches Please Make Every Friday," helping you recall Triangle, Quadrilateral, Pentagon, Hexagon, Heptagon. This foundation is essential for any polygon quiz or polygon quiz questions focusing on shape identification.

  2. Sum of Interior Angles Formula -

    For any n-sided polygon, the sum of its interior angles is (n - 2) × 180°, so a hexagon's interior angles add to (6 - 2)×180°=720°. This formula, cited by universities like MIT OpenCourseWare, lets you quickly verify angle totals on your polygon properties quiz. Practicing this in sample problems ensures confidence when those tricky interior-angle questions appear.

  3. Exterior Angle Theorem -

    In any simple polygon, the sum of the exterior angles is always 360°, which means each exterior angle in a regular n-gon measures 360°/n. For instance, in a regular octagon, each exterior angle is 360°/8=45°, as shown in geometry resources from Khan Academy. This theorem is a staple of geometry quiz polygons and helps you identify shapes by their turning angles.

  4. Diagonal Count Formula -

    The number of diagonals in an n-sided polygon is given by n(n - 3)/2, so a nonagon has 9×6/2=27 diagonals. Verified by sources like Wolfram MathWorld, this formula lets you tackle "identify polygon shapes" questions that ask for diagonals without drawing the figure. Remembering this quick computation will boost your speed during timed polygon quiz questions.

  5. Regular vs. Irregular Polygons -

    Regular polygons have all sides and interior angles equal, while irregular ones do not, a distinction emphasized by the National Council of Teachers of Mathematics. Recognizing regularity helps you predict symmetry properties and calculate area more easily, often using the formula A = (1/4)n s² cot(π/n) for regular n-gons. Mastering this contrast will sharpen your skills on any polygon properties quiz.

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