Use the polygon sum to find the measure of all the angles, then find the measure of the variable.

(2 points)
Sum of the polygon angles =

u =
°

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1 answer

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.

  1. Determine the number of sides (n): You'll need to know how many sides your polygon has in order to use the formula.

  2. Calculate the Sum of the polygon angles:

    • For example, if you have a hexagon (6 sides): \[ \text{Sum of interior angles} = (6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ \]
  3. 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!