Question

Angles of triangle are un AP. The greatest angle is twice the least​

Answer 1

Answer:

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Answer 2

Let,

required angles are a - d , a and a + d, since they are in arithmetic progression.

From the properties of triangles :

sum of all angles of a triangle is 180°.

Thus,

→ ( a - d ) + a + ( a + d ) = 180°

→ a - d + a + a + d = 180°

→ 3a = 180°

→ a = 60°

Given,

Greatest angle is twice the least.

→ greatest angle = 2 x least angle

→ a + d = 2( a - d )

→ a + d = 2a - 2d

→ d + 2d = 2a - a

→ 3d = a

→ 3d = 60° (from above, a = 60°)

→ d = 20°

Therefore, angles are :

>> a - d = 60° - 20° = 40°

>> a = 60°

>> a + d = 60° + 20° = 80°

Hence the required angles are 40° , 60° and 80°