Question

Find the measure of each angle in Triangle ABC. m∠a=(40x−21)°m∠b=(31−2x)°m∠c=(x+14)°

Answer 1

Answer:

  D. m∠a=139°, m∠b=23°, m∠c=18°

Step-by-step explanation:

This is a multiple-choice question that can be answered simply by considering the reasonableness of the answers.

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The expression for ∠a suggests it will be by far the largest of the angles, eliminating choices A and C.

No angle in a triangle is more than 180°, eliminating choice B.

The expression for ∠b suggests it will have a measure less than 31°. This confirms choice D as the correct one.

  m∠a=139°, m∠b=23°, m∠c=18°

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If you want to work the problem, you use the fact that the sum of angles is 180°

  ∠a +∠b +∠c = 180°

  (40x -21)° +(31 -2x)° +(x +14)° = 180°

  39x +24 = 180 . . . . . . . . . divide by °, collect terms

  39x = 156 . . . . . . . . . . subtract 24

  x = 4 . . . . . . . . . . . divide by 39

Then the measures of the angles are ...

  ∠a = (40×4 -21)° = 139°

  ∠b = (31 -2×4)° = 23°

  ∠c = (4 +14)° = 18°