Nthe figure, and are line segments. what is the sum of x and y? 108° 116° 118° 126°

The sum of x and y are 116 degrees.   X=54 degrees and y=62 degrees.

Explanation 

in point o they have 2 angles that are vertical to each other meaning that they are congruent to each other.   One of the angles is 64 degrees so the other angle that is vertical to it would be 64 degrees also.   So, if we have the two triangles that have 2 angles we can know the last remaining angles since the triangles would need to add to 180 degrees.   In triangle 1,  we have 62 degrees and 64 degrees.  We add them together to get 126 and we subtract 126 from 180 degrees to get the last angle which is 54 degrees.   Moving on to the next triangle.  We have 64 degrees and 54 degrees.  We add them together and get 118 and we subtract 118 from 180 to get 62 degrees.  Now that we found out that x=54 and y-62 we add them together and we get 116.

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