Polygons: Essential Concepts for Competitive Exam Success

Polygons

Q. If a polygon has 8 sides, what is the measure of each interior angle in a regular octagon?

A. 135 degrees
B. 120 degrees
C. 108 degrees
D. 150 degrees

Solution

The measure of each interior angle of a regular polygon can be calculated using the formula [(n-2) * 180] / n. For an octagon (n=8), it is [(8-2) * 180] / 8 = 135 degrees.

Correct Answer: C — 108 degrees

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Q. If a polygon has 8 sides, what is the sum of its interior angles?

A. 720 degrees
B. 1080 degrees
C. 900 degrees
D. 1440 degrees

Solution

The sum of the interior angles of an octagon (8-sided polygon) is calculated using the formula (n-2) * 180, which gives (8-2) * 180 = 1080 degrees.

Correct Answer: B — 1080 degrees

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Q. If the exterior angle of a regular polygon is 30 degrees, how many sides does it have?

A. 6
B. 12
C. 10
D. 8

Solution

The sum of the exterior angles of any polygon is 360 degrees. Therefore, the number of sides can be calculated as 360 / 30 = 12.

Correct Answer: B — 12

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Q. If the perimeter of a regular hexagon is 72 cm, what is the length of each side?

A. 10 cm
B. 12 cm
C. 14 cm
D. 8 cm

Solution

The perimeter of a regular hexagon is the sum of the lengths of its 6 equal sides. Therefore, each side is 72 cm / 6 = 12 cm.

Correct Answer: B — 12 cm

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Q. In a certain polygon, the exterior angle at each vertex measures 45 degrees. How many sides does this polygon have?

A. 4
B. 5
C. 8
D. 10

Solution

The sum of the exterior angles of any polygon is 360 degrees. If each exterior angle is 45 degrees, the number of sides is 360 / 45 = 8.

Correct Answer: C — 8

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Q. In a regular dodecagon, what is the measure of each exterior angle?

A. 30 degrees
B. 36 degrees
C. 24 degrees
D. 18 degrees

Solution

The measure of each exterior angle of a regular polygon is 360/n. For a dodecagon (n=12), it is 360/12 = 30 degrees.

Correct Answer: B — 36 degrees

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Q. In a regular pentagon, what is the measure of each interior angle?

A. 108 degrees
B. 120 degrees
C. 90 degrees
D. 72 degrees

Solution

The measure of each interior angle in a regular pentagon can be calculated using the formula (n-2) * 180 / n, which results in (5-2) * 180 / 5 = 108 degrees.

Correct Answer: A — 108 degrees

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Q. In the context of geometry, which of the following statements about polygons is true?

A. All polygons are convex.
B. A polygon can have an infinite number of sides.
C. The sum of the interior angles of a polygon increases with the number of sides.
D. All polygons are regular.

Solution

The sum of the interior angles of a polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides. Therefore, as the number of sides increases, the sum of the interior angles also increases.

Correct Answer: C — The sum of the interior angles of a polygon increases with the number of sides.

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Q. What is the minimum number of sides a polygon can have?

A. 2
B. 3
C. 4
D. 5

Solution

The minimum number of sides a polygon can have is 3, which is a triangle.

Correct Answer: B — 3

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Q. Which of the following best describes a regular polygon?

A. A polygon with all sides of different lengths.
B. A polygon with all angles equal and all sides equal.
C. A polygon that can be inscribed in a circle.
D. A polygon with at least one angle greater than 180 degrees.

Solution

A regular polygon is defined as a polygon where all sides and angles are equal, making option 2 the correct description.

Correct Answer: B — A polygon with all angles equal and all sides equal.

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Q. Which of the following is NOT a characteristic of a regular polygon?

A. All sides are of equal length.
B. All interior angles are equal.
C. It can have an odd number of sides.
D. It can be concave.

Solution

A regular polygon is defined as a polygon with all sides and angles equal, and it cannot be concave; it must be convex.

Correct Answer: D — It can be concave.

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Q. Which of the following is NOT a property of polygons?

A. Polygons are two-dimensional shapes.
B. Polygons can have curved sides.
C. Polygons are made up of straight line segments.
D. Polygons can be classified as regular or irregular.

Solution

Polygons are defined as shapes made up of straight line segments, so having curved sides disqualifies a shape from being a polygon.

Correct Answer: B — Polygons can have curved sides.

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Q. Which of the following polygons cannot be classified as a convex polygon?

A. A square
B. A rectangle
C. A concave hexagon
D. An equilateral triangle

Solution

A concave hexagon has at least one interior angle greater than 180 degrees, which makes it a non-convex polygon.

Correct Answer: C — A concave hexagon

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Q. Which of the following polygons is classified as a concave polygon?

A. Square
B. Regular pentagon
C. Star-shaped polygon
D. Equilateral triangle

Solution

A star-shaped polygon has at least one interior angle greater than 180 degrees, making it concave.

Correct Answer: C — Star-shaped polygon

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Q. Which of the following statements about the diagonals of a polygon is correct?

A. A triangle has no diagonals.
B. A quadrilateral has two diagonals.
C. A pentagon has five diagonals.
D. A hexagon has nine diagonals.

Solution

A triangle has no diagonals, as it has only three vertices. The formula for the number of diagonals in a polygon is n(n-3)/2, where n is the number of sides.

Correct Answer: A — A triangle has no diagonals.

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Q. Which of the following terms best describes a polygon with all sides and angles equal?

A. Irregular polygon
B. Convex polygon
C. Regular polygon
D. Concave polygon

Solution

A polygon with all sides and angles equal is known as a regular polygon.

Correct Answer: C — Regular polygon

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Polygons

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