What is the sum of the interior angle of a regular nonagon? Select one: ? a. 1550° ? b. 1440° ? c. 1350° ? d. 1260°
The Correct Answer and Explanation is:
The correct answer is d. 1260°.
To determine the sum of the interior angles of any polygon, you can use a standard formula. This formula is applicable whether the polygon is regular (having equal sides and angles) or irregular. The formula is:
Sum of interior angles = (n – 2) × 180°
In this formula, ‘n’ represents the number of sides of the polygon.
The question asks for the sum of the interior angles of a regular nonagon. A nonagon is a polygon with nine sides. Therefore, for this problem, n = 9.
Now, we can substitute the value of ‘n’ into the formula:
- Start with the formula: Sum = (n – 2) × 180°
- Substitute n = 9: Sum = (9 – 2) × 180°
- Perform the subtraction inside the parentheses: Sum = 7 × 180°
- Multiply 7 by 180 to find the final sum: Sum = 1260°
The logic behind this formula is that any polygon can be divided into a number of triangles by drawing diagonals from a single vertex. The number of triangles you can create is always two less than the number of sides (n – 2). Since the sum of angles in any triangle is always 180°, you can find the total sum of the polygon’s angles by multiplying the number of triangles by 180°. For a nine-sided nonagon, you can create 7 triangles, leading to the calculation 7 × 180°.
Comparing our calculated result of 1260° with the given options:
a. 1550°
b. 1440°
c. 1350°
d. 1260°
The result matches option d, confirming it is the correct answer.
