https://file.aiquickdraw.com/mathbot/file/1726442185596ontnl57f.jpg

Let's analyze the image and work through the questions step by step.

### Given Information:
- Polygon B is a scaled copy of Polygon A.
- Some sides and angles of the polygons are marked with numbers, while others are marked with question marks, indicating they are unknown.

### Part (a): What is the scale factor from Polygon A to Polygon B?
The given sides are:
- Polygon A: One side is 1.5 units.
- Polygon B: The corresponding side is 5 units.

The scale factor is calculated as:
\[
\text{Scale Factor} = \frac{\text{Side length in Polygon B}}{\text{Side length in Polygon A}} = \frac{5}{1.5} = \frac{10}{3} \approx 3.33
\]
So, the scale factor from Polygon A to Polygon B is \( \frac{10}{3} \), or approximately 3.33.

### Part (b): Find the missing lengths of the sides marked with "?" in Polygon B.
- Polygon A has a side of 2.5 units. Using the scale factor, the corresponding side in Polygon B will be:
  \[
  2.5 \times \frac{10}{3} = \frac{25}{3} \approx 8.33 \text{ units}
  \]
- The other side in Polygon A is unknown (marked with a "?"). The corresponding side in Polygon B is also unknown, but once you solve for one, you can apply the scale factor to find the other.

### Part (c): Determine the measure of each angle marked with a "?" in Polygon A.
- Since Polygon B is a scaled copy of Polygon A, the angles in both polygons are identical.
- In Polygon B, two angles are given: \( 53^\circ \) and \( 82^\circ \).
- The sum of the interior angles of a quadrilateral is \( 360^\circ \). Therefore, the sum of the remaining two angles is:
  \[
  360^\circ - (53^\circ + 82^\circ) = 360^\circ - 135^\circ = 225^\circ
  \]
  So, the remaining two angles in Polygon B (and hence Polygon A) must add up to \( 225^\circ \). Since Polygon A is similar, the corresponding angles will have the same measure.

Would you like more detailed explanations or further clarification? Here are five related questions for practice:

1. How would you find the perimeter of Polygon B using the scale factor?
2. How does the scale factor affect the area of Polygon B compared to Polygon A?
3. Can you determine the length of the unknown side in Polygon A based on the given information?
4. What is the relationship between the interior angles of a scaled polygon and the original polygon?
5. How would the problem change if Polygon B were scaled down instead of up?

### Tip: When polygons are scaled, all corresponding angles remain equal, and all corresponding side lengths are proportional to the scale factor.

What is the scale factor from Polygon A to Polygon B? Find the missing length of each side marked with a '?' in Polygon B. Determine the measure of each angle marked with a '?' in Polygon A.

Learn how to find the scale factor between two polygons, calculate missing side lengths, and determine the unknown angles in a geometric scaling problem. This problem involves key concepts in geometry such as proportions, scale factor, and the Angle-Sum Theorem for quadrilaterals, suitable for Grade 7-8 students.

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