Answer:
(x, y) = (13, -18)
Explanation:
You want the values of x and y given vertical angles labeled (8x-34)° and (10x-60°), while their supplements are labeled (7y+236)° and (4y+182)°.
Vertical angles
Vertical angles are congruent, so we can equate the expressions for the same angle measure:
(10x -60)° = (8x -34)° . . . . . . angles facing left and right
2x = 26 . . . . . . . . divide by °, add 60-8x
x = 13 . . . . . . . . divide by 2
These angles are ...
(10x -60)° = (10·13 -60)° = 70°
The other pair of angles is ...
(7y +236)° = (4y +182)° . . . . . angles facing up and down
3y = -54 . . . . . . . . . . . divide by °, subtract 4y+236
y = -18 . . . . . . . . . . divide by 3
These angles are ...
(4y +182)° = (4(-18) +182)° = 110° . . . . . . supplementary to the others
The values of x and y are 13 and -18, respectively.