Answer:
1) 9 sides
2) 135°
3) 7 sides
Explanation:
Question 1
To find the number of sides of a polygon, given the sum of its interior angles, we can use the formula:

where:
- S is the sum of the interior angles.
- n is the the number of sides of the polygon.
Given that the sum of the measures of the interior angles is 1260° substitute S = 1260° into the formula and solve for n:

Therefore, the polygon has 9 sides.

Question 2
To find the measure of each interior angle of a regular octagon, we can use the formula:

where n is the number of sides of the polygon.
The number of sides of a regular octagon is 8. Therefore, substitute n = 8 into the formula:

Therefore, the measure of each interior angle of a regular octagon is 135°.

Question 3
To find the number of sides of a polygon given the sum of its interior angles, we can use the formula:

where:
- S is the sum of the interior angles.
- n is the the number of sides of the polygon.
Given that the sum of the measures of the interior angles is 900°, substitute S = 900° into the formula and solve for n:

Therefore, the polygon has 7 sides.