The sum of seven interior angles of 1000°. Find the eighth angle. Octagon is? Please answer step by step fast, please. I have to complete my work for my school.
The Correct Answer and Explanation is:
We are given:
- The sum of seven interior angles of an octagon is 1000°.
- We are to find the eighth angle.
✅ Step-by-step Solution:
Step 1: Understand the problem
An octagon has 8 sides, so it has 8 interior angles.
We are given the sum of 7 of these angles = 1000°, and we are to find the eighth.
Step 2: Use the formula for the sum of interior angles
For any polygon with n sides, the sum of interior angles is:Sum=(n−2)×180∘\text{Sum} = (n – 2) \times 180^\circSum=(n−2)×180∘
For an octagon (n = 8):Sum=(8−2)×180=6×180=1080∘\text{Sum} = (8 – 2) \times 180 = 6 \times 180 = 1080^\circSum=(8−2)×180=6×180=1080∘
So, the total sum of all 8 interior angles of an octagon is 1080°.
Step 3: Subtract the sum of the 7 known angles
We are told that the sum of seven interior angles = 1000°
So, the eighth angle = 1080° – 1000° = 80°
✅ Final Answer:
80∘\boxed{80^\circ}80∘
Explanation (No em dashes):
An octagon is a polygon with eight sides. Every polygon has a total interior angle sum that depends on the number of sides it has. The formula to find the total interior angle sum is to take the number of sides, subtract two, and multiply the result by 180 degrees. This rule comes from dividing the polygon into triangles. Each triangle contributes 180 degrees to the total angle sum.
For an octagon, we apply the formula like this: (8 – 2) × 180 = 6 × 180 = 1080 degrees. This means that if we add up all eight interior angles of an octagon, we should get 1080 degrees.
In this problem, we are told that seven of the interior angles already add up to 1000 degrees. Since the total for all eight is 1080 degrees, we can subtract the known sum of seven angles from the total. So, 1080 degrees minus 1000 degrees equals 80 degrees. This is the missing eighth angle.
This approach is based purely on geometry and works for any polygon. You can always find a missing angle if you know the total interior angle sum and the values of the other angles. This method helps not only with octagons but also with other shapes like pentagons, hexagons, or decagons. It is important to understand and remember the basic formula for interior angle sums. Once you know that, solving problems like this becomes easy and fast.
