What is the sum of 6 of the interior angles of a regular octagon?
The Correct Answer and Explanation is:
The correct answer is 810°.
To find the sum of 6 of the interior angles of a regular octagon, we first need to determine the measure of a single interior angle. The problem specifies a “regular octagon,” which tells us two key things. First, an octagon is a polygon that has eight sides (n=8). Second, the term “regular” means that all its sides are of equal length and all its interior angles have the same measure. This uniformity is essential for the calculation.
The first step is to calculate the sum of all the interior angles of an octagon. We can use the standard formula for the sum of the interior angles of any polygon, which is (n – 2) × 180°, where ‘n’ is the number of sides. For an octagon, n is 8.
Applying the formula:
Sum of all interior angles = (8 – 2) × 180°
Sum = 6 × 180°
Sum = 1080°
This result, 1080°, represents the total measure of all eight interior angles combined.
Since the octagon is regular, all eight of its interior angles are identical. To find the measure of just one of these angles, we divide the total sum by the number of angles, which is 8.
Measure of one interior angle = Total Sum / Number of Angles
Measure of one interior angle = 1080° / 8
Measure of one interior angle = 135°
Now we know that each interior angle of a regular octagon measures 135°.
The final step is to calculate the sum of 6 of these identical angles. We simply multiply the measure of a single angle by 6.
Sum of 6 interior angles = 6 × (Measure of one interior angle)
Sum of 6 interior angles = 6 × 135°
Sum of 6 interior angles = 810°
Thus, the sum of six of the interior angles of a regular octagon is 810 degrees.
