What is the value of x?

Step-by-step explanation:

Step One

Find the supplement of both exterior angles. They both have angles that add with them to make 180 degrees.

x + 105 = 180            Subtract 105 from both sides

x = 180 - 105

x = 75

y + 148 = 180            Subtract 148 from both sides

y = 180 - 148  

y = 32

Step Two

There are two ways to conclude the problem. You could find the value of the 3rd angle of the triangle, or you could notice that x is going to be the sum of the 2 angles you just found. These two angles are called the remote interior angle.

Method One

x = 32 + 75

x = 107

Method Two

32 + 75 + y = 180

107 + y = 180

y = 180 - 107

y = 73

The sum of x + 73 = 180

x = 180 - 73

x = 107

-6 is the correct option from the above given options