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We are given a hexagon with angles measuring 100°, 130°, 155°, 75°, 110°, and \( n \). Our task is to find \( n \).

### Step 1: Sum of interior angles of a hexagon
The formula for the sum of the interior angles of a polygon is:

\[
\text{Sum of angles} = 180(n-2)
\]

For a hexagon, \( n = 6 \), so:

\[
\text{Sum of angles} = 180(6-2) = 180 \times 4 = 720^\circ
\]

### Step 2: Add up the known angles
We are given the angles: 100°, 130°, 155°, 75°, and 110°. Let’s add these:

\[
100 + 130 + 155 + 75 + 110 = 570^\circ
\]

### Step 3: Calculate \( n \)
Now, subtract the sum of the given angles from the total sum:

\[
n = 720 - 570 = 150^\circ
\]

Thus, the unknown angle \( n \) is \( 150^\circ \).

Would you like further details or have any questions?

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Here are five related questions to expand on this concept:
1. What is the formula for the sum of exterior angles of any polygon?
2. How do you find the measure of one interior angle in a regular hexagon?
3. How do the interior and exterior angles of a hexagon relate to each other?
4. Can a hexagon have an interior angle greater than 180°? Why or why not?
5. How would the sum of interior angles change if we had an octagon instead of a hexagon?

**Tip:** The sum of interior angles increases by 180° with each additional side in a polygon.

A hexagon has angles that measure 100°, 130°, 155°, 75°, 110°, and n. What is n?

Learn how to find the unknown angle in a hexagon with given angles: 100°, 130°, 155°, 75°, 110°. Understand the sum of interior angles of a hexagon, using the formula (n-2) * 180°, and solve for the missing angle n.

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