Question

The angle of triangle are in ap. the least being half the greatest find the angle.

Answer 1

let the angles be a-d,a,a+d
according to the question a+d = 2(a-d)
a-d+a+a+d = 180 (since sum of the angles are 180 degrees )
= 3a = 180
= a = 60
from second equation 3d = 60
d = 20
so the angles are 40 60 and 80

Answer 2

Answer:

The measure of angles are 20, 60, 100.

Step-by-step explanation:

It is given that the angles are in AP.

Let the angles be a-d, a and a+d.

The sum of angles is 180 degree.

$a-d+a+a+d=180$

$3a=180$

$a=60$

The value of a is 60.

The least being half the greatest find the angle.

$a-d=\frac{1}{2}(a+d)$

$2a-2d=a+d$

$2a-a=2d+d$

$a=3d$

$60=3d$

$d=20$

The value of d is 20.

Therefore, the measure of angles are 20, 60, 100.