The measure of the largest exterior angle of hexagon is 105
Solution:
Given, The measures of 5 of the Interior angles of a hexagon are: 115.125", 85", 150", and 170".
We have to find what is the measure of the largest exterior angle?
Now let us find the 6th interior angle,
We know that, sum of interior angles of hexagon = 720 degrees
115 + 125 + 85 + 150 + 170 + 6th angle = 720
645 + 6th angle = 720
6th angle = 720 – 645
6th angle = 75 degrees
Now we have to find the largest exterior angle, we know that, the complement of largest exterior angle will be smallest interior angle.
So, here smallest interior angle is 75
sum of interior and exterior angle equals to 180
Hence interior angle + exterior angle =180
Then, 75 + exterior angle = 180
Exterior angle = 180 – 75 = 105.
Hence, exterior angle is 105 and 1st option is correct.