Question

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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Answer 1

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!