In triangle abc, the measure of angle b is 42° more than three times the measure of angle a. the measure of angle c is 63° more than the measure of angle a. find the measure of each angle.

B = 42 +3A
C = 63 +A
A +B +C = 180 . . . . . . these are 3 angles of a triangle

Substitute for B and C in the last equation.
A +(42 +3A) +(63 +A) = 180
5A = 75 . . . . . . . . . . . . . . . . . collect terms, subtract 105
A = 15 . . . . . . . . . . . . . . . . . . divide by 5
B = 42 +3*15 = 87
C = 63 +15 = 78

The measures of the angles are
  A = 15°
  B = 87°
  C = 78°


Check
15 +87 +78 = 180
102 +78 = 180
180 = 180 . . . . . . . answers check OK

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