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In the context of geometry, which of the following statements about polygons is

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Question: In the context of geometry, which of the following statements about polygons is true?

Options:

  1. All polygons are convex.
  2. A polygon can have an infinite number of sides.
  3. The sum of the interior angles of a polygon increases with the number of sides.
  4. All polygons are regular.

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

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.

In the context of geometry, which of the following statements about polygons is

Practice Questions

Q1
In the context of geometry, which of the following statements about polygons is true?
  1. All polygons are convex.
  2. A polygon can have an infinite number of sides.
  3. The sum of the interior angles of a polygon increases with the number of sides.
  4. All polygons are regular.

Questions & Step-by-Step Solutions

In the context of geometry, which of the following statements about polygons is true?
  • Step 1: Understand what a polygon is. A polygon is a shape with straight sides, like a triangle or a square.
  • Step 2: Identify the number of sides in the polygon. This is represented by 'n'. For example, a triangle has 3 sides, a square has 4 sides.
  • Step 3: Use the formula to find the sum of the interior angles of the polygon. The formula is (n-2) * 180 degrees.
  • Step 4: Calculate the sum of the interior angles for different values of n. For example, for a triangle (n=3), the sum is (3-2) * 180 = 180 degrees.
  • Step 5: Notice that as 'n' (the number of sides) increases, the sum of the interior angles also increases. For example, for a pentagon (n=5), the sum is (5-2) * 180 = 540 degrees.
  • Interior Angles of Polygons – The sum of the interior angles of a polygon can be calculated using the formula (n-2) * 180 degrees, where n is the number of sides.
  • Relationship Between Sides and Angles – As the number of sides of a polygon increases, the sum of its interior angles also increases.
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