Since l and m are parallel, the unlabeled angle adjacent to the 63° one also has measure (7x - 31)° (it's a pair of alternating interior angles).
Then the three angles nearest line m are supplementary so that
(7x - 31)° + 63° + (5x - 8)° = 180°
Solve for x :
(7x - 31) + 63 + (5x - 8) = 180
12x + 24 = 180
12x = 156
x = 13
The bottom-most angle labeled with measure (4y + 27)° is supplementary to the angle directly adjacent to it, so this unlabeled angle has measure 180° - (4y + 27)° = (153 - 4y)°. The interior angles of any triangle have measures that sum to 180°, so we have
(7x - 31)° + 63° + (153 - 4y)° = 180°
We know that x = 13, so 7x - 31 = 60. Then this simplifies to
123° + (153 - 4y)° = 180°
Solve for y :
123 + (153 - 4y) = 180
276 - 4y = 180
96 = 4y
y = 24
