Two-page geometry worksheet focusing on calculating exterior angles of regular polygons.

Since I can't view or access images directly, I’ll help you solve the problems based on the text you’ve provided. The worksheet is titled "Polygons: Exterior Angles", and it contains several questions about exterior and interior angles of polygons. Let's go through each question step by step.

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Question 1:

> By extending the sides of these shapes, produce all of the exterior angles. You should have 18 exterior angles. Measure each and label the angle with its size. What is the sum of the exterior angles in the equilateral triangle? What about the hexagon and the nonagon? What do you notice?

Solution:

- For any polygon, the sum of the exterior angles is always 360°, regardless of the number of sides.
- This applies to:
- Equilateral triangle: Sum of exterior angles = 360°
- Regular hexagon: Sum of exterior angles = 360°
- Regular nonagon (9 sides): Sum of exterior angles = 360°

✔ What you notice:
The sum of the exterior angles of any polygon is always 360°.

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Question 2:

> What is the size of an exterior angle of a regular octagon? Use this information to find the size of an interior angle in a regular octagon.

Step-by-step:

- A regular octagon has 8 sides.
- Since the sum of exterior angles is 360°, each exterior angle =
$$
\frac{360^\circ}{8} = 45^\circ
$$

- Interior angle + Exterior angle = 180° (they are supplementary)
So, interior angle =
$$
180^\circ - 45^\circ = 135^\circ
$$

✔ Answer:
- Exterior angle = 45°
- Interior angle = 135°

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Question 3:

> What is the size of an exterior angle of a regular decagon? Use this information to find the size of an interior angle in a regular decagon.

- A regular decagon has 10 sides.
- Each exterior angle =
$$
\frac{360^\circ}{10} = 36^\circ
$$
- Interior angle =
$$
180^\circ - 36^\circ = 144^\circ
$$

✔ Answer:
- Exterior angle = 36°
- Interior angle = 144°

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Question 4:

> A regular polygon has exterior angles of 30°. What is the size of each interior angle in this polygon?

Step-by-step:

- Exterior angle = 30°
- Interior angle =
$$
180^\circ - 30^\circ = 150^\circ
$$

✔ Answer:
- Interior angle = 150°

(Also, you could find the number of sides:
$$
\frac{360^\circ}{30^\circ} = 12 \text{ sides (dodecagon)}
$$)

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Question 5:

> A regular polygon has interior angles of 170°. How many sides does it have?

Step-by-step:

- Interior angle = 170°
- So, exterior angle =
$$
180^\circ - 170^\circ = 10^\circ
$$
- Number of sides =
$$
\frac{360^\circ}{10^\circ} = 36
$$

✔ Answer:
- The polygon has 36 sides.

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✔ Summary of Answers:

| Question | Answer |
|--------|--------|
| 1 | Sum of exterior angles = 360° for all polygons |
| 2 | Exterior angle = 45°, Interior angle = 135° |
| 3 | Exterior angle = 36°, Interior angle = 144° |
| 4 | Interior angle = 150° |
| 5 | Number of sides = 36 |

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