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°
