In the context of geometry, which of the following statements about polygons is true?
Practice Questions
1 question
Q1
In the context of geometry, which of the following statements about polygons is true?
All polygons are convex.
A polygon can have an infinite number of sides.
The sum of the interior angles of a polygon increases with the number of sides.
All polygons are regular.
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.
Questions & Step-by-step Solutions
1 item
Q
Q: In the context of geometry, which of the following statements about polygons is true?
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.
Steps: 5
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.
