SOLUTION: the angles of a triangle area in ap if the smallest angles is 40 find the angles of the triangle

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Question 795737: the angles of a triangle area in ap if the smallest angles is 40 find the angles of the triangle
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the smallest angle measures 40%5Eo, and the measures of the angles are in arithmetic progression, the measures of the angles (in degrees) must be
40, 40%2Bd, and 4%2B2d,
with d= common difference between consecutive terms of the arithmetic progression.

Since the measures of all 3 angles of a triangle add up to 180%5Eo,
40%2B%2840%2Bd%29%2B%2840%2B2d%29=180
40%2B40%2Bd%2B40%2B2d=180
120%2Bd%2B2d=180
120%2B3d=180
3d=180-120
3d=60
d=60%2F3
d=20

So the measures of the angles (in degrees) are:
highlight%2840%29 (as given)
40%2Bd=40%2B20=highlight%2860%29, and
40%2B2d=40%2B2%2A20=40%2B40=highlight%2880%29

NOTE:
AP or ap may be commonly understood to mean arithmetic progression in some countries, but in the USA, AP means Advanced Placement (courses and exams), and arithmetic progressions are called arithmetic sequences.
Math is almost a universal language, but not quite.