Question

The angles of a triangle are in A.P., the least being half the greatest. Find the angles.​

Answer 1

Answer:

The required angles are 40°, 60° and 80°

Explanation:

The explanation is given as attachment.

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Answer 2

let the least angle of the triangle be "a"

let the 2nd angle be "b"

then as per condition,

the greatest angle = 2a

=> a + b + 2a = 180 (angle property of triangle)

=> 3a + b = 180 .....................eq.1

since the angles a , b , 2a are in ap

therefore we can write

=> b - a = 2a - b

=> 2b = 3a

=> 3a - 2b = 0.............................eq.2

solving equation 1 and 2 we get

3a + b = 180

3a - 2b = 0

___________

3b = 180

b = 60°

using equation 1 we get

=> 3a + 60 = 180

=> 3a = 120

=> a = 40°

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