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Quizzes > High School Quizzes > Mathematics

Polygon Practice Quiz: Test Your Geometry Skills

Gear up with interactive questions and examples

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Colorful paper art promoting the Polygon Power Challenge, a middle school geometry quiz.

What is a polygon?
A closed plane figure with at least three straight sides.
A figure with no sides or curves.
A three-dimensional object.
A curved figure with no angles.
A polygon is defined as a closed plane figure with straight sides that are connected end-to-end. It has at least three sides, which distinguishes it from curves or open figures.
Which of the following is a polygon?
A circle
An ellipse
A triangle
A spiral
A triangle has three straight sides and closed vertices, which qualifies it as a polygon. The other options either have curves or do not form a closed figure with straight lines.
How many sides does a regular pentagon have?
4
5
6
7
A pentagon, by definition, has five sides. The term 'regular' implies that all sides and angles are equal.
What is the sum of the interior angles of a triangle?
90 degrees
180 degrees
360 degrees
270 degrees
The interior angles of any triangle always add up to 180 degrees. This is a fundamental property taught in basic geometry.
Identify the property that all sides of a regular polygon share.
They are unequal.
They are perpendicular.
They are of equal length.
They are curved.
A regular polygon is defined by having all sides of equal length and all interior angles equal. This uniformity is what distinguishes it from irregular polygons.
What formula can be used to find the sum of the interior angles of an n-sided polygon?
n × 180
(n - 2) × 180
(n + 2) × 180
180 ÷ n
The sum of the interior angles of a polygon with n sides is given by (n - 2) × 180 degrees. This formula works by dividing the polygon into (n-2) triangles.
In a regular hexagon, each interior angle measures:
120 degrees
90 degrees
60 degrees
150 degrees
A hexagon has 6 sides, so its interior angle sum is (6 - 2) × 180 = 720 degrees. Dividing 720 by 6 gives 120 degrees per interior angle in a regular hexagon.
How many diagonals does an octagon have?
16
20
24
28
The number of diagonals in a polygon is calculated using the formula n(n - 3)/2. For an octagon (n = 8), this gives 8 × 5 / 2 = 20 diagonals.
Which of the following statements is true about a regular polygon?
Only one angle is congruent.
All angles are congruent.
Sides are of different lengths.
It has only one line of symmetry.
A regular polygon is characterized by having all sides and all interior angles equal. This uniformity ensures complete symmetry in the shape.
Calculate the measure of each exterior angle of a regular decagon.
36 degrees
35 degrees
45 degrees
40 degrees
The sum of the exterior angles of any polygon is 360 degrees. For a decagon with 10 sides, each exterior angle is 360 ÷ 10 = 36 degrees.
Which of the following does NOT qualify as a quadrilateral?
Square
Rectangle
Triangle
Trapezoid
A quadrilateral must have four sides. A triangle only has three sides, so it does not qualify as a quadrilateral, unlike the other options provided.
Which property distinguishes a convex polygon from a concave polygon?
All interior angles are less than 180 degrees.
At least one interior angle is exactly 180 degrees.
It has more than four sides.
Its sides are all parallel.
Convex polygons have all interior angles less than 180 degrees, ensuring no indentations. In contrast, a concave polygon has at least one interior angle greater than 180 degrees.
In a regular polygon, if one interior angle is 150 degrees, how many sides does the polygon have?
12
6
10
8
Using the formula for the interior angle of a regular polygon, ((n - 2) × 180) ÷ n = 150. Solving the equation gives n = 12, which means the polygon is a dodecagon.
Which type of polygon has all sides and angles equal, making it the most symmetrical?
Irregular polygon
Trapezoid
Regular polygon
Scalene polygon
A regular polygon is defined by having all sides and interior angles equal, resulting in maximum symmetry. This property is what differentiates it from irregular polygons.
What is the measure of an exterior angle of a regular hexagon?
60 degrees
90 degrees
120 degrees
30 degrees
For any regular polygon, the exterior angles sum to 360 degrees. In a hexagon, dividing 360 by 6 results in each exterior angle measuring 60 degrees.
For a convex polygon with 15 sides, what is the sum of its interior angles?
2340 degrees
2160 degrees
2520 degrees
2700 degrees
The sum of the interior angles of a polygon is determined by the formula (n - 2) × 180. For a 15-sided polygon, (15 - 2) × 180 equals 2340 degrees.
Determine the number of diagonals in a regular dodecagon (12-sided polygon).
54
48
60
72
A dodecagon has 12 sides. Using the formula for diagonals, n(n - 3)/2, we compute 12 × (12 - 3) ÷ 2 = 54 diagonals.
A regular polygon has each interior angle measuring 156 degrees. How many sides does it have?
15
12
18
10
Setting up the interior angle formula ((n - 2) × 180) ÷ n = 156 and solving for n results in n = 15. This indicates that the polygon is a 15-sided figure.
If a polygon has an exterior angle of 10 degrees at each vertex and is regular, how many sides does it have?
18
36
72
20
A regular polygon's exterior angles sum to 360 degrees. Dividing 360 by the given 10 degrees per vertex results in 36 sides.
Consider a polygon whose interior angles form an arithmetic sequence. Which of the following must be true?
The polygon is necessarily regular.
The common difference must be zero.
The average interior angle is equal to that of a regular polygon with the same number of sides.
The sum of any two consecutive angles is constant.
Even when the interior angles form an arithmetic sequence, the fixed total sum forces their average to equal the interior angle of a regular polygon with the same number of sides. However, this does not imply that all angles are equal unless the common difference is zero.
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Study Outcomes

  1. Understand the properties of different polygons, including their sides and angles.
  2. Analyze the differences between regular and irregular polygons.
  3. Apply formulas to calculate perimeters and interior angles of various polygons.
  4. Synthesize polygon concepts to solve geometric problems confidently.

Polygon Quiz Practice Test Cheat Sheet

  1. Define a polygon - A polygon is a closed, two-dimensional shape formed by straight line segments that meet at vertices. From triangles and quadrilaterals to decagons and beyond, each polygon's name hints at how many edges it has. Knowing this helps you spot patterns in geometry and makes naming shapes feel like solving a fun puzzle. GeeksforGeeks
    2. GeeksforGeeks: Polygon Formula
  2. Calculate interior angles - To find the sum of a polygon's interior angles, use (n‑2) × 180°, where "n" is the number of sides. For example, a pentagon (5 sides) packs in 540° total, so you can feel angles adding up nicely. This formula lets you check your work and keep angular surprises at bay. GeeksforGeeks
    3. GeeksforGeeks: Polygon Formula
  3. Sum of exterior angles - Every polygon, no matter how many sides, has exterior angles summing to 360°. You can walk around the perimeter turning at each corner, and you'll make one full circle by the time you're done. It's a neat trick to check crazy shapes and keep your math mojo strong. GeeksforGeeks
    4. GeeksforGeeks: Polygon Formula
  4. Regular vs. irregular polygons - A regular polygon is like the popular kid: all its sides and angles are the same. Irregular shapes mix it up with sides or angles of different sizes, making them less predictable but super interesting to analyze. Spotting the difference is the first step in tackling shape-based challenges. GeeksforGeeks
    5. GeeksforGeeks: Polygon Formula
  5. Area of regular polygons - To find the area of a regular polygon, use (Perimeter × Apothem) ÷ 2. The apothem is the line from the center straight down to the middle of a side, turning perimeter measurements into an area party. Once you know the perimeter and apothem, calculating space inside is as easy as snapping your fingers. GeeksforGeeks
    6. GeeksforGeeks: Polygon Formula
  6. Count diagonals with ease - Use n(n‑3)/2 to figure out how many diagonals a polygon has, where "n" is the side count. A hexagon (6 sides) shows off 9 sweet diagonals cutting across its center, which you can use to divide shapes into triangles. Counting diagonals helps you break down polygons into simpler building blocks. GeeksforGeeks
    7. GeeksforGeeks: Polygon Formula
  7. Convex vs. concave - Convex polygons keep every interior angle under 180°, so they look like perfectly puffed-up balloons. Concave polygons have at least one interior angle over 180°, creating a cool "caved-in" effect or a star-like appearance. Spotting concave dents helps you avoid miscalculations when applying formulas. GeeksforGeeks
    8. GeeksforGeeks: Polygon Formula
  8. Parallelogram properties - In a parallelogram, opposite sides are always equal and parallel, opposite angles match, and the diagonals cut each other in half. These relationships turn tricky proofs into a series of "aha!" moments. Use these rules to solve area and angle puzzles in a flash. Online Math Learning
    9. Online Math Learning: Properties of Polygon
  9. Trapezoid essentials - A trapezoid has at least one pair of parallel sides called bases, and in an isosceles trapezoid, the non-parallel legs match in length, making base angles congruent. This symmetry leads to awesome shortcuts for finding angles and areas. Knowing your trapezoids means mastering a slice of quadrilateral territory. Online Math Learning
    10. Online Math Learning: Properties of Polygon
  10. Geometry mnemonics - Memory tricks like "Cherry pie's delicious!" for circumference (C=π×d) and "Apple pies are too!" for area (A=π×r²) turn complex formulas into tasty bites. These fun phrases stick in your brain, making exam prep feel more like snack time. Mix, match, and craft your own catchy lines to become a formula-fueled wizard. Online Math Learning
    11. Online Math Learning: Mnemonics for Geometry
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