The measures of 5 of the interior angles of a hexagon are: 130°, 120°, 80°, 160°, and 155°. What is the measure of the largest exterior angle?
100°
105°
95°
90°
To find the measure of the largest exterior angle of a hexagon, we need to know that the sum of the measures of all the exterior angles of any polygon, regardless of the number of sides, is always 360 degrees.
In a hexagon, there are six interior angles and six corresponding exterior angles. The interior and exterior angles are related as follows: the interior and exterior angles at any vertex add up to 180 degrees.
Let's find the sum of the measures of the interior angles given:
130° + 120° + 80° + 160° + 155° = 645°
Since a hexagon has six interior angles, we can calculate the measure of the sixth interior angle by subtracting the sum of the given interior angles from the total sum for a hexagon: 360° - 645° = -285°
However, since angles cannot have negative measures, we can assume that the sixth angle is positive by simply taking its absolute value: 285°
Now, to find the measure of the largest exterior angle, we subtract the value of the corresponding interior angle from 180°:
180° - 285° = -105°
Again, angles cannot have negative measures, so we take the absolute value to make it positive: 105°
Therefore, the measure of the largest exterior angle is 105°. So, none of the given options (100°, 105°, 95°, 90°) is correct.