Question

the angle of triangle are in AP the least being half the greater. find the angle​

Answer 1

Sum of all angles of a triangle is 180°

The measures of angles of the triangles

are in AP - - - - - - - - - - - - (given)

Let t1=a be the first angle, t2 the second t3 the third.

d is the common difference =t3 -

t3=1/2 t3=t2/2

Sn=n/2 [2a + (n-1) d]

S3=180=3/2 [2a +(3-1) (t3-t2)]

180=1.5[2a + 2(t2/2-t2)]

180=1.5[2a+ 2(t2-2t2/t2)]

180=1.5[2a+2(-t2/t2)]

180=1.5[2a+2 (-1)]

180=1.5[2a-2]

180=3a - 3

180+3=3a

183=3a

a=183/3

a=61

Thus, first angle = a =61°

Third angle = half of second angle