Question

The measures of 5 of the Interior angles of a hexagon are: 115.125", 85", 150", and 170". What is the measure of the

Answer 1

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.