To find the other angle of an octagon when one of the angles is 156 degrees, we can start by recalling that a regular octagon has 8 angles. In a regular octagon, all angles are equal. However, if you state that one angle is 156 degrees and want to find the other angles that are equal to it, we can use the following steps:
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Calculate the total sum of the interior angles of the octagon: The formula for the sum of the interior angles of a polygon is \((n - 2) \times 180\), where \(n\) is the number of sides. For an octagon (\(n = 8\)): \[ \text{Sum of angles} = (8 - 2) \times 180 = 6 \times 180 = 1080 \text{ degrees} \]
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Find how many angles equal 156 degrees: Let \(x\) be the number of angles that are 156 degrees. As stated that the other angle is also equal, we can assume that there are \(x\) angles of 156 degrees and \(y\) other angles. Since there are a total of 8 angles, we have: \[ x + y = 8 \]
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Calculate the remaining angle: The total sum of the angles can also be expressed as: \[ 156x + A \cdot y = 1080 \] where \(A\) is the measure of the other equal angle.
Given that \(y = 8 - x\): Replacing \(y\) in the sum equation: \[ 156x + A(8 - x) = 1080 \] Simplifying this gives us: \[ 156x + 8A - Ax = 1080 \] \[ (156 - A)x + 8A = 1080 \]
If we are looking for when \(x = y\):
- Typically, if both angles are equal (let's assume all angles must be equal for simplicity), then we can directly use: \[ 7x + 156 = 1080 \] which leads to solving for \(x\): \[ 7x = 1080 - 156 \] \[ 7x = 924 \] \[ x = 924 / 7 = 132 \]
So if one angle of an octagon is 156 degrees, the others would not be the same, but in a context where we look for equal angle settings, the entire configuration would imply: Other angle = 132 degrees.