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Quizzes > High School Quizzes > Mathematics

Polygons Worksheet: Practice Quiz

Build Polygon Mastery With Engaging Practice Exercises

Difficulty: Moderate
Grade: Grade 6
Study OutcomesCheat Sheet
Colorful paper art promoting a Polygon Playground trivia quiz for high school geometry students.

What is a polygon?
A shape with only curved lines
A closed two-dimensional shape with straight sides
An open figure
A three-dimensional object
A polygon is defined as a closed, flat shape made up of straight line segments. The other options do not meet the definition of a polygon.
Which of the following is a quadrilateral?
Triangle
Hexagon
Square
Pentagon
A quadrilateral is a polygon that has exactly four sides. Among the given options, a square is the one with four congruent sides.
What formula is used to calculate the sum of interior angles in an n-sided polygon?
180*(n-2)
180*n
360/(n-2)
360*(n-2)
The sum of the interior angles of an n-sided polygon is given by the formula (n-2)*180. This formula is derived by dividing the polygon into (n-2) triangles.
What defines a regular polygon?
Only the sides are equal
Only the angles are equal
It contains one pair of parallel sides
All sides and angles are equal
A regular polygon has all sides and all interior angles equal, which gives it a high degree of symmetry. The other options describe only part of the properties or unrelated features.
How many sides does a pentagon have?
6
7
5
4
A pentagon, by definition, is a five-sided polygon. The other numbers represent different types of polygons.
What is the measure of each interior angle in a regular hexagon?
150°
100°
90°
120°
A regular hexagon has 6 sides, so the sum of its interior angles is (6-2)*180 = 720°. Dividing 720° by 6 gives 120° per angle. The other options do not satisfy this calculation.
How many diagonals does a pentagon have?
5
10
7
3
The formula for calculating diagonals in an n-sided polygon is n(n-3)/2. For a pentagon, this yields 5*(5-3)/2 = 5 diagonals. The other values do not follow from the formula.
Which characteristic best describes a convex polygon?
It is not a closed figure
At least one interior angle is greater than 180°
All interior angles are less than 180°
It has equal sides and angles
A convex polygon is defined by having all interior angles less than 180°. This ensures that no line segment between two points on the polygon goes outside the shape. The other options either describe concave polygons or irrelevant properties.
What is the sum of the interior angles of a hexagon?
720°
600°
660°
540°
Using the formula (n-2)*180 for a hexagon (n=6), we get (6-2)*180 = 720°. The other answer choices do not match the formula's output.
Which condition must be met for a polygon to be classified as concave?
At least one interior angle is greater than 180°
It has all sides of equal length
It has no diagonals
All interior angles are less than 180°
A concave polygon has at least one interior angle that is greater than 180°, which creates a 'caved-in' side. The other options describe characteristics of convex or regular polygons.
What is the measure of one exterior angle in a regular octagon?
90°
45°
60°
30°
The sum of exterior angles for any polygon is 360°. In a regular octagon, dividing 360° by 8 gives 45° per exterior angle. The other options do not correctly divide the total measure.
Which polygon has no diagonals?
Triangle
Hexagon
Square
Pentagon
A triangle, having only 3 sides, does not have any diagonals since there are no non-adjacent vertices. The other polygons have at least one diagonal.
If a polygon's interior angles sum to 1080°, how many sides does it have?
9
10
8
7
Using the formula (n-2)*180 = 1080°, we solve for n: n-2 = 1080/180 = 6, so n = 8. The other numbers do not satisfy the equation.
What property is essential for classifying a polygon as regular?
All sides and interior angles are congruent
Only the diagonals are equal
Only the interior angles are equal
Only opposite sides are parallel
For a polygon to be classified as regular, all its sides and interior angles must be congruent. This property ensures symmetry and uniformity that the other options do not provide.
How many lines of symmetry does a regular pentagon possess?
2
5
4
3
A regular pentagon has 5 lines of symmetry, each passing through a vertex and the midpoint of the opposite side. The other numbers underestimate the amount of symmetry present in a regular pentagon.
A polygon has 14 diagonals. How many sides does it have?
5
6
8
7
Using the formula for the number of diagonals, n(n-3)/2 = 14, we get n(n-3) = 28. Testing n = 7 gives 7×4 = 28, which is correct. The other options do not satisfy the equation.
The measure of each exterior angle of a regular polygon is 20°. How many sides does the polygon have?
18
15
20
16
Since the sum of the exterior angles of any polygon is 360°, dividing 360° by an exterior angle of 20° gives 18 sides. The other options do not meet this division.
In a regular polygon, the difference between an interior angle and its corresponding exterior angle is 140°. How many sides does the polygon have?
16
20
18
15
For any polygon, the interior and exterior angles are supplementary, meaning they add up to 180°. If their difference is 140°, then 180 - 2E = 140, which implies E = 20°. Dividing 360° by 20° results in 18 sides. The other options do not work with this reasoning.
A regular polygon's interior angle is five times its exterior angle. How many sides does the polygon have?
15
12
8
10
Let the exterior angle be x. Then the interior angle is 180 - x, and according to the problem, 180 - x = 5x. Solving gives 6x = 180, so x = 30°. The number of sides is 360/30 = 12. The other choices do not satisfy this equation.
If a polygon has one interior angle measuring 190°, what can be deduced about the polygon?
It is concave
It has all equal sides
It is regular
It is convex
An interior angle that measures more than 180° indicates that the polygon is concave, as it has an indentation. The other options imply properties that are not possible when an interior angle exceeds 180°.
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Study Outcomes

  1. Identify and classify various polygons based on their side lengths and angles.
  2. Analyze the relationships between interior and exterior angles of polygons.
  3. Calculate the sum of interior and exterior angles for different polygons.
  4. Apply geometric properties to solve problems related to polygon configurations.
  5. Evaluate symmetry and congruence in polygon structures.

Worksheet for Polygons Cheat Sheet

  1. Definition of Polygons - Polygons are flat, two-dimensional shapes made by connecting straight line segments end to end. Regular polygons take symmetry seriously: all their sides and angles are exactly the same, making them look super neat and predictable. Ready to dive deeper? Math Is Fun
  2. Sum of Interior Angles - To find the total degrees inside any polygon, use the formula (n − 2) × 180°, where n is the number of sides. This nifty equation tells you how "angle-packed" your shape is - perfect for impressing friends in geometry class. Byju's
  3. Sum of Exterior Angles - No matter how many sides your polygon has, if you walk all the way around and keep turning at each corner, you'll turn a full 360° in total. It's like taking a complete spin around a merry‑go‑round - you always end up facing the start! Revision Maths
  4. Angles in Regular Polygons - In a regular polygon, each exterior angle is simply 360°÷n, and each interior angle is 180°−(360°÷n). This means equal slices of an angle‑pie - slice size depends on how many sides you cut it into. Math Is Fun
  5. Area of Regular Polygons - You can calculate the area with (1/2) × n × s² × sin(360°/n), where s is the side length and n is the number of sides. It's like breaking the shape into equal triangles, finding each area, then adding them up for the grand total. Byju's
  6. Divide into Triangles - Splitting any polygon into triangles is a classic trick to simplify angle and area calculations. With triangles you know the rules (sum of angles = 180°), making the whole shape's secrets easier to unlock! Revision Maths
  7. Common Polygon Names - Get friendly with triangle (3 sides), quadrilateral (4), pentagon (5), hexagon (6) and beyond. Knowing the names is the first step to recognizing them everywhere: in honeycombs, traffic signs, and even cool art! Revision Maths
  8. Triangle's Interior Angles - Every triangle's interior angles add up to 180°, no exceptions. This fundamental rule is the backbone for many proofs and helps when you split larger polygons into triangular pieces. GeeksforGeeks
  9. Quadrilateral and Pentagon Angles - Quadrilaterals always sum to 360° and pentagons to 540°. Once you know the pattern, you can predict the total interior angle sum of any polygon by plugging into that trusty (n−2)×180° formula. Math Warehouse
  10. Equal Angles in Regular Polygons - In regular polygons, all interior angles are the same, so each is simply the total interior sum divided by n. It's like sharing pizza slices equally - everyone gets the same angle! Byju's
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