Question

the angles of a triangle are in arithmetic progression. If one of the angle is hundred degrees what are the measures of other two angles.

Answer 1

The angles are in AP Let the angle be ,a ,(a+d) ,(a+2d) One angle is 100 degree a + (a+d) + (a+2d) =180 ....... Measure of all angles of a triangle is 180 degree  a+ a + d+ a + 2 d = 180 3a + 3d = 180 3(a+d) = 180 a+d = 60 100+ d = 60 .....a=100 d= - 40  Angles are a= 100 a+d = 100+(-40)  = 60 degree a +2d = 100 +2(-40) = 100-80                                   = 20 degree Therefore the measure of angles are 100,60,20