Question

the angles of a triangle are in AP .the greatest angle is twice the least . find the angles

Answer 1

let the angles be a-d,a,a+d
given,2(a-d)=a+d
2a-2d=a+d
2a-a-2d-d=0
a=3d eq1
we know that,
(a-d)+a+(a+d)=180
3a=180
a=60
put a=60 in eq1
d=a/3
d=60/3
d=20
angles are a-d=60-20=40°
a=60°
a+d=60+20=80°

Answer 2

Hey there ☻ !

Let the angles of a triangle be a , b, c.

Here, c is the greatest angle, and a being the smallest .

Now,According to the question,

c = 2 a.

Also,c - b = b - a

Substituting,

2a - b = b - a

2a + a = b + b

3a = 2b

b = 3a/2

Now, We know that,Sum of angles of a triangle = 180°a + b + c = 180°a + 3a/2 + 2a = 180a ( 1 + 3/2 + 2 ) = 180a ( 3 + 3/2 ) = 180a ( 9/2 ) = 180a = 360 / 9 = 40

Now,c = 2 ( 40 ) = 80

b = 3/2 * ( 40 ) = 60

Therefore the angles of the triangle are 40 , 60 , 80°