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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

x= 149. 24+7=31. 180-31=149

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