Question

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

Answer 1

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 = 180

a ( 1 + 3/2 + 2 ) = 180

a ( 3 + 3/2 ) = 180

a ( 9/2 ) = 180

a = 360 / 9 = 40

Now,

c = 2 ( 40 ) = 80

b = 3/2 * ( 40 ) = 60

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