Answer:
The sum of the interior angles of any polygon with n sides can be found using the formula:
sum = (n - 2) x 180°
We can use this formula to find the sum of the interior angles of the polygon with 5 known angles:
sum = (5 - 2) x 180°
sum = 3 x 180°
sum = 540°
We know that the sum of all interior angles of a polygon is equal to the sum of its individual interior angles. Therefore, we can subtract the sum of the 5 known angles from the total sum to find the size of the final unknown interior angle:
sum of unknown angle = total sum - sum of known angles
sum of unknown angle = 540° - (162° + 115° + 125° + 148° + 105°)
sum of unknown angle = 540° - 655°
sum of unknown angle = -115°
This result does not make sense because an interior angle of a polygon must be a positive value.
We can check our work by using another formula that gives the size of each interior angle of a polygon with n sides:
size of each interior angle = (n - 2) x 180° / n
If we assume that the polygon has 6 sides (which is a valid assumption since any polygon with 5 sides or more can have different combinations of interior angles), we can use this formula to find the size of each interior angle:
size of each interior angle = (6 - 2) x 180° / 6
size of each interior angle = 4 x 180° / 6
size of each interior angle = 120°
We can then check if our 5 known angles add up to 600° (5 x 120°). If they do, then we have the correct value for the size of each interior angle, and we can use it to find the size of the final unknown angle:
sum of known angles = 162° + 115° + 125° + 148° + 105°
sum of known angles = 655°
We see that the sum of the known angles is not equal to 600°, which means that our assumption of the polygon having 6 sides was incorrect. In fact, the polygon must have more than 6 sides since the sum of the known angles is greater than the sum of the angles of a hexagon (which is 720°).
Therefore, we cannot find the size of the final unknown interior angle without more information about the polygon.
Explanation:
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