Final answer:
The polygon in question has 10 sides, making the sum of its interior angles 1440°.
Step-by-step explanation:
To calculate the sum of the interior angles of a polygon, we first need to determine the number of sides the polygon has.
The sum of the angles in any polygon can be found using the formula (n - 2) × 180°, where n is the number of sides.
In this question, we have three angles given: 125°, 140°, and 160°.
The remaining angles are all 145° each.
Let's denote the number of 145° angles as x.
We can set up the equation:
125° + 140° + 160° + (145° × x) = (x + 3 - 2) × 180°
Simplifying both sides and solving for x gives us the number of sides of the polygon:
- 425° + (145°×x) = (1 + x)× 180°
- 425° + 145°×x = 180° + 180°×x
- 145°×x - 180°×x = 180° - 425°
- -35°×x = -245°
- x = 7
Therefore, the polygon has 7 + 3 = 10 sides.
The sum of the interior angles will be:
(10 - 2) × 180°
= 8 × 180°
= 1440°.