Angles in Polygons Worksheets - Free Printable

It looks like you've uploaded an image of a worksheet titled "Angles in Polygons", which asks students to find the measure of the indicated angles in various polygons. However, since I can't view or access images directly, I can't see the specific diagrams or problems.

But I can help you solve this type of problem if you describe the polygons and the angles shown in the image.

Here’s how we typically solve these types of problems:

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🔷 Step-by-Step Approach for "Angles in Polygons"

#### 1. Sum of Interior Angles
For any polygon with $ n $ sides:
$$
\text{Sum of interior angles} = (n - 2) \times 180^\circ
$$

#### 2. Regular Polygon (All sides and angles equal)
If the polygon is regular:
$$
\text{Each interior angle} = \frac{(n - 2) \times 180^\circ}{n}
$$

#### 3. Exterior Angles
The sum of exterior angles of any polygon is always $ 360^\circ $. For a regular polygon:
$$
\text{Each exterior angle} = \frac{360^\circ}{n}
$$

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🔷 Common Examples

Let’s suppose the worksheet includes:

- Triangle (3 sides): Sum = $ (3-2)\times180 = 180^\circ $
- Quadrilateral (4 sides): Sum = $ (4-2)\times180 = 360^\circ $
- Pentagon (5 sides): Sum = $ 540^\circ $
- Hexagon (6 sides): Sum = $ 720^\circ $

If a polygon is regular, divide the total by the number of sides to get each angle.

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🔷 Example Problem

Suppose one question shows a regular pentagon and asks for the measure of one interior angle.

$$
\text{Interior angle} = \frac{(5 - 2) \times 180^\circ}{5} = \frac{540^\circ}{5} = 108^\circ
$$

So, the answer would be $ \boxed{108^\circ} $

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🔷 How You Can Help Me Solve It

Please describe the polygons in the image, such as:

- Number of sides
- Whether they are regular or irregular
- Any given angles
- Which angle is being asked for (e.g., marked with a letter or question mark)

Or, if you can copy-paste the text or describe the figures, I’ll walk you through solving each one step by step.

Let me know!