To find the sum of the interior angles of a polygon, you can use the formula:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
where \( n \) is the number of sides of the polygon.
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Determine the number of sides (n): You'll need to know how many sides your polygon has in order to use the formula.
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Calculate the Sum of the polygon angles:
- For example, if you have a hexagon (6 sides): \[ \text{Sum of interior angles} = (6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ \]
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Find the measure of the variable (u): Once you know the sum of the angles, you can use this value to solve for the angle represented by the variable \( u \). The equation will depend on the specific angles in your polygon.
For example, if you have a polygon with angles given by four expressions:
- \( u \)
- \( 2u \)
- \( 3u \)
- \( 4u \)
Then you can set up the equation: \[ u + 2u + 3u + 4u = \text{Sum of interior angles} \] \[ 10u = 720^\circ \quad (\text{from the hexagon example}) \] \[ u = \frac{720^\circ}{10} = 72^\circ \]
If you can provide the specific number of sides or angles in your polygon, I can help calculate the measures more precisely!