One angle of an eight-sided polygon is `100^(@)` and the other angles are equal. Find the measure of each equal angle.

Answer

To solve the problem, we need to find the measure of each equal angle in an eight-sided polygon (octagon) when one angle is given as \(100^\circ\) and the other angles are equal.

### Step-by-Step Solution:

1. **Determine the Sum of Interior Angles**:
The formula for the sum of the interior angles of a polygon with \(n\) sides is given by:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
For an octagon (\(n = 8\)):
\[ \text{Sum of interior angles} = (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ \]

**Hint**: Remember that the sum of the interior angles increases with the number of sides.

2. **Set Up the Equation**:
Let the measure of each of the equal angles be \(x\). Since one angle is \(100^\circ\) and there are 7 equal angles, we can write the equation:
\[ 100^\circ + 7x = 1080^\circ \]

**Hint**: Ensure that you account for all angles in the polygon when setting up your equation.

3. **Solve for \(x\)**:
Rearranging the equation gives:
\[ 7x = 1080^\circ - 100^\circ \]
\[ 7x = 980^\circ \]
Now, divide both sides by 7:
\[ x = \frac{980^\circ}{7} = 140^\circ \]

**Hint**: When dividing, make sure to perform the division carefully to avoid mistakes.

4. **Conclusion**:
Each of the equal angles in the octagon measures \(140^\circ\).

**Final Answer**: Each equal angle is \(140^\circ\).