The polygon shown in the image has an irregular shape. Let's answer the two parts of the question:

a) How many sides does the polygon have?

From the image, we can count the sides of the polygon. It appears to have 8 sides, making it an octagon. Even though it's not regular (since all sides and angles are not necessarily equal), it is still an octagon due to having 8 sides.

b) What is the sum of its interior angles?

The sum of the interior angles of a polygon can be calculated using the formula: $\text{Sum of interior angles} = (n - 2) \times 180^\circ$ Where $n$ is the number of sides.

For an 8-sided polygon: $\text{Sum of interior angles} = (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ$

So, the sum of the interior angles of this polygon is 1080 degrees.

Summary:

• a) The polygon has 8 sides.
• b) The sum of its interior angles is 1080°.

Would you like further details or have any questions?

Here are 5 follow-up questions for practice:

1. How would you calculate the measure of each interior angle if the polygon were regular?
2. What is the difference between regular and irregular polygons?
3. Can you explain how the formula for the sum of interior angles was derived?
4. If the polygon had 12 sides, what would be the sum of its interior angles?
5. How do exterior angles relate to interior angles in polygons?

Tip: To find the measure of a single interior angle in a regular polygon, divide the sum of interior angles by the number of sides.