Question 795737
If the smallest angle measures {{{40^o}}}, and the measures of the angles are in arithmetic progression, the measures of the angles (in degrees) must be
{{{40}}}, {{{40+d}}}, and {{{4+2d}}},
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^o}}},
{{{40+(40+d)+(40+2d)=180}}}
{{{40+40+d+40+2d=180}}}
{{{120+d+2d=180}}}
{{{120+3d=180}}}
{{{3d=180-120}}}
{{{3d=60}}}
{{{d=60/3}}}
{{{d=20}}}
 
So the measures of the angles (in degrees) are:
{{{highlight(40)}}} (as given)
{{{40+d=40+20=highlight(60)}}}, and
{{{40+2d=40+2*20=40+40=highlight(80)}}}
 
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.