Find the values of x and y for which the lines are parallel. a.) x = 40, y = 53 b.) x = 78, y = 53 c.) x = 53, y = 78 d.) x = 78, y = 55

The apex If the triangle is 40, bc it's alternate interior with 40, due to the parallel lines.
Now all angles sum 180 in a triangle:
y+10 + 77 + 40 = 180
y + 127 = 180
y +137 -127 = 180-127
y = 53
Now the y+10 + 40 + x-1 sum to 180 2nd they all make a straight line:
x-1 + 40 + 53+10 = 180
x + 102 = 180
x + 102 -102 = 180-102
x = 78
Therefore the correct answer is:
B.) x = 78, y = 53