the sum of seven interior angles of an octagon is 1000 Find the right angle ? With step
The Correct Answer and Explanation is:
To find the missing interior angle (the “right angle”) of an octagon when the sum of the other seven interior angles is 1000 degrees, we can follow these steps:
Step-by-step solution
- Recall the formula for the sum of interior angles of a polygon:
Sum of interior angles=(n−2)×180\text{Sum of interior angles} = (n – 2) \times 180Sum of interior angles=(n−2)×180
For an octagon, n=8n = 8n=8:Sum=(8−2)×180=6×180=1080 degrees\text{Sum} = (8 – 2) \times 180 = 6 \times 180 = 1080 \text{ degrees}Sum=(8−2)×180=6×180=1080 degrees
- Subtract the sum of the seven given angles from the total:
We are told that the sum of seven interior angles is 1000 degrees. So the remaining one interior angle (the one we need to find) is:Missing angle=1080−1000=80 degrees\text{Missing angle} = 1080 – 1000 = 80 \text{ degrees}Missing angle=1080−1000=80 degrees
Final Answer:
The remaining interior angle is 80 degrees.
Explanation (no em dashes)
To solve this problem, we need to understand the geometry of an octagon and how interior angles are calculated. An octagon is a polygon with eight sides. One important property of polygons is that the sum of all their interior angles depends on the number of sides. The formula to find this sum is:(n−2)×180(n – 2) \times 180(n−2)×180
Here, nnn is the number of sides. For an octagon, n=8n = 8n=8, so the total sum of its interior angles is:(8−2)×180=6×180=1080 degrees(8 – 2) \times 180 = 6 \times 180 = 1080 \text{ degrees}(8−2)×180=6×180=1080 degrees
This means that if we add all eight interior angles of any octagon, we will get 1080 degrees.
In the question, we are told that seven of these angles already add up to 1000 degrees. To find the missing eighth angle, we subtract the sum of the known seven angles from the total:1080−1000=80 degrees1080 – 1000 = 80 \text{ degrees}1080−1000=80 degrees
Therefore, the remaining angle must be 80 degrees.
This problem illustrates how geometric properties and algebra work together. Even without knowing the individual values of the seven angles, just their sum is enough to find the eighth angle. It is not a right angle, since a right angle is always 90 degrees. Instead, the missing angle is an acute angle, because it is less than 90 degrees.
