in triangle ABC
m \angle B = ( \frac{1}{3} ) m \angle A --------- ( 1 )
m \angle C = m \angle A - 37 ------------ ( 2 )
the sum of the internal angles of a triangle = 180
thus
m \angle A + m \angle B + m \angle C = 180 ----------- ( 3 )
compensate from ( 1 ) and ( 2 ) in ( 3 )
m \angle A + ( \frac{1}{3} ) m \angle A + ( m \angle A - 37 ) = 180
( \frac{7}{3} ) m \angle A - 37 = 180 ( add 37 to both sides )
( \frac{7}{3} ) m \angle A = 180 + 37 = 217 ( multiply both sides by ( \frac{3}{7} )
m \angle A = 217 ( \frac{3}{7} ) = 31 x 3 = 93
m \angle A = 93
compensate in ( 1) by m \angle A = 93
m < B = ( 1 / 3 ) x 93 = ( 93 / 3 ) = 31
compensate in ( 2 ) by m < A = 93
m \angle C = 93 - 37 = 56
thus
m \angle A = 93
m \angle B = 31
m < C = 56
answer
measures of the angles of the triangle ABC :
m \angle A = 93
m \angle B = 31
m \angle C = 56